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2024 (4)

An Accurate and Efficient Recursive Convolution Method to Simulate Viscoacoustic and Viscoelastic Waves. Jin, C.; Zhou, B.; Greenhalgh, S.; Jamal Zemerly, M.; Kamel Riahi, M.; and Cao, D. IEEE Transactions on Geoscience and Remote Sensing, 62. 2024. Cited by: 0

An Accurate and Efficient Recursive Convolution Method to Simulate Viscoacoustic and Viscoelastic Waves [link]

Paper doi link bibtex abstract

@ARTICLE{Jin2024,
	author = {Jin, Chao and Zhou, Bing and Greenhalgh, Stewart and Jamal Zemerly, Mohamed and Kamel Riahi, Mohamed and Cao, Danping},
	title = {An Accurate and Efficient Recursive Convolution Method to Simulate Viscoacoustic and Viscoelastic Waves},
	year = {2024},
	journal = {IEEE Transactions on Geoscience and Remote Sensing},
	volume = {62},
	doi = {10.1109/TGRS.2024.3393613},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85191892470&doi=10.1109%2fTGRS.2024.3393613&partnerID=40&md5=2d82b3ba81850c830e63ca8acca67743},
	abstract = {Seismic wavefield forward modeling in anelastic (attenuating) media is a fundamental tool for both data processing and interpretation in modern seismic exploration. We propose a generalized recursive convolution (RC) formula to calculate the temporal convolutions directly, rather than solving many auxiliary partial differential equations of the memory variables when dealing with a viscoelastic medium. The new formula is obtained in terms of the Taylor series expansion and offers approximations of the convolutions to arbitrary order by the number of terms retained. We conduct theoretical and numerical comparisons of the new method with the commonly used memory variable method and other traditional RC methods. The comparisons show that the new method has the highest accuracy of all these RC methods and yields better performance with various stress relaxation times and time steps than the common leapfrog time-stepping scheme to solve the auxiliary partial differential equations of the memory variables. Our numerical examples verify the versatility and feasibility of the new method for viscoacoustic and viscoelastic wave modeling.  © 1980-2012 IEEE.},
	note = {Cited by: 0}
}

A generalized time-domain velocity-stress seismic wave equation for composite viscoelastic media with a topographic relief and an irregular seabed. Jin, C.; Zhou, B.; Riahi, M. K.; and Zemerly, M. J. Computational Geosciences, 28(3): 355 – 371. 2024. Cited by: 1

Paper doi link bibtex abstract

@ARTICLE{Jin2024355,
	author = {Jin, Chao and Zhou, Bing and Riahi, Mohamed Kamel and Zemerly, Mohamed Jamal},
	title = {A generalized time-domain velocity-stress seismic wave equation for composite viscoelastic media with a topographic relief and an irregular seabed},
	year = {2024},
	journal = {Computational Geosciences},
	volume = {28},
	number = {3},
	pages = {355 – 371},
	doi = {10.1007/s10596-024-10273-2},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85183905177&doi=10.1007%2fs10596-024-10273-2&partnerID=40&md5=39dc5ab993038d5e179efe6dc562fd5f},
	abstract = {Accurate seismic wave modeling of viscoelastic anisotropic medium is a fundamental tool for seismic data processing, interpretation and full waveform inversion. Also, free water surface, topographic relief and irregular seabed are often encountered in practical seismic surveys. Thus, basing on the General Maxwell Body, we proposed a generalized matrix form of the velocity-stress seismic wave equation, which becomes valid for composite viscoelastic anisotropic media and satisfies the boundary conditions in presence of topographic free surfaces and irregular fluid–solid interfaces. We theoretically show that the viscoelastic effect of a medium may be considered as the intrinsic body sources accumulated in wavefield history and computed by a recursive convolution formula accurately and efficiently. We also demonstrated that such a generalized viscoelastic wave equation may be solved with the curvilinear MacCormack finite difference method and validated the accuracy and feasibility of the proposed method. The modeling results in homogeneous and heterogeneous media match well with the analytical solutions and the references yielded by the spectral element solutions. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.},
	note = {Cited by: 1}
}

On cost-efficient parallel iterative solvers for 3D frequency-domain seismic multisource viscoelastic anisotropic wave modeling. Ma, G.; Zhou, B.; Riahi, M. K.; Zemerly, J.; and Xu, L. Geophysics, 89(4): T151 – T162. 2024. Cited by: 0

On cost-efficient parallel iterative solvers for 3D frequency-domain seismic multisource viscoelastic anisotropic wave modeling [link]

Paper doi link bibtex abstract

@ARTICLE{Ma2024T151,
	author = {Ma, Guoqi and Zhou, Bing and Riahi, Mohamed Kamel and Zemerly, Jamal and Xu, Liu},
	title = {On cost-efficient parallel iterative solvers for 3D frequency-domain seismic multisource viscoelastic anisotropic wave modeling},
	year = {2024},
	journal = {Geophysics},
	volume = {89},
	number = {4},
	pages = {T151 – T162},
	doi = {10.1190/geo2023-0368.1},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85195794773&doi=10.1190%2fgeo2023-0368.1&partnerID=40&md5=75b7faad96fc9a9becb8768f218d761a},
	abstract = {Solving large sparse linear systems in 3D frequency-domain seismic wave modeling, especially in viscoelastic anisotropic media, poses significant challenges due to the increasing number of discrete moduli and nonzero elements in the linear system matrix. The computational load surpasses that of acoustic or viscoacoustic media, making it even more challenging when dealing with multisource problems. Popular scientific tools for solving a linear system, such as multifrontal massively parallel sparse direct solver (MUMPS), structured matrix package (STRUMPACK), and portable extensible toolkit for scientific computation (PETSc), can be used, but their applicability to our specific problem has not been comprehensively evaluated. Our study aims to tackle the challenges in solving large, sparse, complex-valued symmetric linear systems with multiple right-hand side vectors for 3D frequency-domain seismic wave modeling. We have adopted the preconditioned conjugate gradient iterative algorithms as the foundation for our research, introducing two highly cost-effective parallel iterative solvers: the parallel symmetric successive overrelaxation conjugate gradient (P-SSORCG) and the parallel incomplete Cholesky conjugate gradient (P-ICCG). These novel solvers are subjected to a comprehensive comparative analysis against well-established scientific tools, such as MUMPS, STRUMPACK, and PETSc, in the context of 3D frequency-domain seismic wave modeling. We show their promising performances in a practical 3D SEG/EAGE overthrust model and demonstrate that the grouped P-SSORCG offers an efficient alternative to parallel direct solvers, particularly in situations wherein computational resources are limited.  © 2024 Society of Exploration Geophysicists.},
	note = {Cited by: 0}
}

On the numerical resolution of the second-order viscoacoustic and viscoelastic anisotropic wave equations using the recursive convolution method. Jin, C.; Zhou, B.; Riahi, M. K.; Zemerly, M. J.; and Cao, D. Computers and Geosciences, 184. 2024. Cited by: 0

Paper doi link bibtex abstract

@ARTICLE{Jin2024,
	author = {Jin, Chao and Zhou, Bing and Riahi, Mohamed Kamel and Zemerly, Mohamed Jamal and Cao, Danping},
	title = {On the numerical resolution of the second-order viscoacoustic and viscoelastic anisotropic wave equations using the recursive convolution method},
	year = {2024},
	journal = {Computers and Geosciences},
	volume = {184},
	doi = {10.1016/j.cageo.2024.105538},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85183580613&doi=10.1016%2fj.cageo.2024.105538&partnerID=40&md5=c8487bd0c3eeed84a258489bf7cd174b},
	abstract = {Accurate and efficient seismic wave modeling is fundamental for the high-resolution seismic full-waveform inversion and correct interpretation of seismic data. Based on the viscoelastic mechanism of the Generalized Standard Linear Solid and the constitutive relationship between stress and strain, we demonstrate a generalized recursive formula using the Taylor series expansion to directly compute the temporal convolution in the constitutive equation, rather than solving auxiliary differential equations of the memory variables in the conventional method. New sets of the second order viscoacoustic and viscoelastic anisotropic wave equations are established with the new recursive temporal convolutions, which completely replaces the traditional auxiliary differential equations of the memory variables. The error analysis shows the proposed method can offer better accuracy than the existing recursive methods, and is very competitive with the widely used memory variable method. The numerical results comparing the different methods show the accuracy and feasibility of the generalized recursive convolution method to simulate the viscoacoustic and viscoelastic anisotropic waves. © 2024 Elsevier Ltd},
	note = {Cited by: 0}
}

2023 (7)

Integration of a Gaussian quadrature grid discretization approach with a generalized stiffness reduction method and a parallelized direct solver for 3-D frequency-domain seismic wave modelling in viscoelastic anisotropic media. Ma, G.; Zhou, B.; Greenhalgh, S.; Liu, X.; Zemerly, J.; and Riahi, M. K. Geophysical Journal International, 233(2): 1372 – 1386. 2023. Cited by: 3; All Open Access, Bronze Open Access

Paper doi link bibtex abstract

@ARTICLE{Ma20231372,
	author = {Ma, Guoqi and Zhou, Bing and Greenhalgh, Stewart and Liu, Xu and Zemerly, Jamal and Riahi, Mohamed Kamel},
	title = {Integration of a Gaussian quadrature grid discretization approach with a generalized stiffness reduction method and a parallelized direct solver for 3-D frequency-domain seismic wave modelling in viscoelastic anisotropic media},
	year = {2023},
	journal = {Geophysical Journal International},
	volume = {233},
	number = {2},
	pages = {1372 – 1386},
	doi = {10.1093/gji/ggac503},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85163893276&doi=10.1093%2fgji%2fggac503&partnerID=40&md5=863890239f6448ab761d5b92b5c21e0e},
	abstract = {We integrate three advanced numerical techniques—Gaussian quadrature grid (GQG) discretization, a new generalized stiffness reduction method and the latest version of an efficient parallelized direct solver to achieve accurate 3-D frequency-domain seismic wave modelling in viscoelastic anisotropic media. A GQG is employed to sample and interpolate both model parameters and wavefield quantities as well as to fit with arbitrary free-surface topography and subsurface interfaces of a geological model. A new version of the generalized stiffness reduction method is utilized to effectively remove the artificial boundary edge effects for which the common perfectly matched layer method fails. The most recent version of a multifrontal massively parallel direct solver is applied to tackle the notoriously expensive computation of frequency-domain 3-D wave modelling. We validate the 3-D modelling by comparing with the exact solutions for homogeneous viscoelastic isotropic, vertically transversely isotropic and orthorhombic media. All the results show very close matches between the numerical and analytical solutions. Then, we investigate the computational efficiency of the parallelized direct solver, compare its performance using different ordering schemes, in-core and out-of-core factorization modes and the block low-rank approximation in the factorization for different grid sizes. Our modelling results show that the ordering scheme of the so-called ‘Metis’ is the best for reducing computer memory and run time, and the parallelized direct solver is remarkably faster than iterative solvers for similar workloads but at the expense of higher memory requirements. The out-of-core factorization mode can effectively reduce the memory cost without a compromising on run time. The block low-rank approximation is able to significantly reduce the run time in both the factorization and solving process (up to 56 per cent in total), but will increase the memory cost when using the out-of-core factorization mode. Efficient application of this parallel direct solver should use ‘Metis’ as the ordering scheme and select the out-of-core factorization mode without the block low-rank approximation as the best scheme to save the memory cost, or the in-core factorization mode with the block low-rank approximation for the fastest computation. Finally, we demonstrate the excellent applicability of the 3-D wave modelling scheme for a practical and complex heterogeneous geological model. © The Author(s) 2022.},
	note = {Cited by: 3; All Open Access, Bronze Open Access}
}

We integrate three advanced numerical techniques—Gaussian quadrature grid (GQG) discretization, a new generalized stiffness reduction method and the latest version of an efficient parallelized direct solver to achieve accurate 3-D frequency-domain seismic wave modelling in viscoelastic anisotropic media. A GQG is employed to sample and interpolate both model parameters and wavefield quantities as well as to fit with arbitrary free-surface topography and subsurface interfaces of a geological model. A new version of the generalized stiffness reduction method is utilized to effectively remove the artificial boundary edge effects for which the common perfectly matched layer method fails. The most recent version of a multifrontal massively parallel direct solver is applied to tackle the notoriously expensive computation of frequency-domain 3-D wave modelling. We validate the 3-D modelling by comparing with the exact solutions for homogeneous viscoelastic isotropic, vertically transversely isotropic and orthorhombic media. All the results show very close matches between the numerical and analytical solutions. Then, we investigate the computational efficiency of the parallelized direct solver, compare its performance using different ordering schemes, in-core and out-of-core factorization modes and the block low-rank approximation in the factorization for different grid sizes. Our modelling results show that the ordering scheme of the so-called ‘Metis’ is the best for reducing computer memory and run time, and the parallelized direct solver is remarkably faster than iterative solvers for similar workloads but at the expense of higher memory requirements. The out-of-core factorization mode can effectively reduce the memory cost without a compromising on run time. The block low-rank approximation is able to significantly reduce the run time in both the factorization and solving process (up to 56 per cent in total), but will increase the memory cost when using the out-of-core factorization mode. Efficient application of this parallel direct solver should use ‘Metis’ as the ordering scheme and select the out-of-core factorization mode without the block low-rank approximation as the best scheme to save the memory cost, or the in-core factorization mode with the block low-rank approximation for the fastest computation. Finally, we demonstrate the excellent applicability of the 3-D wave modelling scheme for a practical and complex heterogeneous geological model. © The Author(s) 2022.

2.5-D Time-Domain Seismic Wavefield Modeling in Heterogeneous Viscoelastic and Tilted Transversely Isotropic Media (2023). Won, M.; Zhou, B.; Liu, X.; Zemerly, M. J.; Al-Khaleel, M.; and Riahi, M. K. IEEE Transactions on Geoscience and Remote Sensing, 61. 2023. Cited by: 0

2.5-D Time-Domain Seismic Wavefield Modeling in Heterogeneous Viscoelastic and Tilted Transversely Isotropic Media (2023) [link]

Paper doi link bibtex abstract

@ARTICLE{Won2023,
	author = {Won, Moosoo and Zhou, Bing and Liu, Xu and Zemerly, Mohamed Jamal and Al-Khaleel, Mohammad and Riahi, Mohamed Kamel},
	title = {2.5-D Time-Domain Seismic Wavefield Modeling in Heterogeneous Viscoelastic and Tilted Transversely Isotropic Media (2023)},
	year = {2023},
	journal = {IEEE Transactions on Geoscience and Remote Sensing},
	volume = {61},
	doi = {10.1109/TGRS.2023.3333544},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85178025159&doi=10.1109%2fTGRS.2023.3333544&partnerID=40&md5=4ad70887c62809a7db73076a0f49c061},
	abstract = {Accurately modeling seismic wave propagation in complex subsurface structures is not only helpful to understanding seismic data and rock properties but also the fundamental part of seismic full waveform inversion to image subsurface geological structure. 3-D seismic wave modeling is often expensive due to the huge consumption of computer resources. Alternatively, an efficient and accurate 2.5-D wave modeling can be employed for obtaining the 3-D wavefield in a 2-D geological model that is often encountered in practice. We present two advanced numerical methods for the 2.5-D viscoelastic anisotropic wave modeling by integrating three innovations. First, we formulate the 2.5-D viscoelastic anisotropic wave equations, particularly for a heterogeneous tilted transversely isotropic (TTI) medium that represents many sedimentary and igneous rocks of the subsurface. Second, we extend the common memory variable method and propose a new generalized recursive convolution (RC) method to the 2.5-D wave modeling. Third, we demonstrate the real-domain fully parallelized computing of the two methods to gain high computational efficiency of wave modeling. Our calibration experiments validate the accuracy of the proposed methods, and our modeling of a benchmark geological model exhibits the capability of the proposed methods to simulate the 3-D wavefield in a complex 2-D heterogeneous viscoelastic anisotropic medium. Such robust numerical simulations may enhance the characterization of seismic wave propagation and high-resolution subsurface imaging through full-waveform inversion, which is applicable for seismic exploration, the seismological study of the earth's interior, and geohazard detection.  © 1980-2012 IEEE.},
	note = {Cited by: 0}
}

Generalized recursive convolution method for viscoelastic wave modelling. Jin, C.; Zhou, B.; Greenhalgh, S.; Won, M.; Riahi, M.; and Zemerly, M. 2023. Cited by: 3

Generalized recursive convolution method for viscoelastic wave modelling [link]

Paper link bibtex abstract

@CONFERENCE{Jin20231959,
	author = {Jin, C. and Zhou, B. and Greenhalgh, S. and Won, M. and Riahi, M.K. and Zemerly, M.J.},
	title = {Generalized recursive convolution method for viscoelastic wave modelling},
	year = {2023},
	journal = {84th EAGE Annual Conference and Exhibition},
	volume = {3},
	pages = {1959 – 1963},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85180528109&partnerID=40&md5=7f03b0960325f004833f589fa2dc8931},
	abstract = {Seismic wavefield forward modeling in viscoelastic media is fundamental for both data processing and interpretation in seismic exploration. We develop a generalized recursive convolution method to accurately calculate the temporal convolutions, which are required by the constitutive relationship for anelasticity rather than solving many auxiliary partial differential equations of memory variables. The new method is based on a Taylor series expansion of the temporal convolution and is very competitive with the widely-used memory variable method and the conventional recursive convolution methods. We conduct theoretical and numerical comparisons of the new method with the common leapfrog time-stepping memory variable method and other traditional recursive convolution methods. Our numerical examples verify the accuracy of the new method for viscoacoustic and viscoelastic wave modeling. © 2023 84th EAGE Annual Conference and Exhibition. All rights reserved.},
	note = {Cited by: 3}
}

Computations of the slowness vectors in viscoelastic anisotropic media. Zhou, B.; Fadhil, M.; and Riahi, M. K. 2023. Cited by: 0

Computations of the slowness vectors in viscoelastic anisotropic media [link]

Paper link bibtex abstract

@CONFERENCE{Zhou20231954,
	author = {Zhou, B. and Fadhil, M.T. and Riahi, M. Kamel},
	title = {Computations of the slowness vectors in viscoelastic anisotropic media},
	year = {2023},
	journal = {84th EAGE Annual Conference and Exhibition},
	volume = {3},
	pages = {1954 – 1958},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85195562654&partnerID=40&md5=af854d91e391456a2aa9f714fa9d2011},
	abstract = {We present an extension of the conjugate real ray tracing (C-RRT) method to investigate the slowness vectors in viscoelastic anisotropic media, especially computing the real and imaginary components, the homogeneous and inhomogeneous components of the slowness vectors of three wave modes (qP, qSV, qSH). We demonstrate that once the complex moduli of the medium are given these components of the slowness vectors can be calculated by the C-RRT method. We give examples to display the fractions of the imaginary and inhomogeneous components, which play crucial roles in the attenuation of wave propagation. © 2023 84th EAGE Annual Conference and Exhibition. All rights reserved.},
	note = {Cited by: 0}
}

Numerical Fréchet derivatives of the displacement tensor for 2.5-D frequency-domain seismic full-waveform inversion in viscoelastic TTI media. Yang, Q.; Zhou, B.; Engsig, M.; Won, M.; Riahi, M. K.; Al-khaleel, M.; and Greenhalgh, S. Near Surface Geophysics, 21(6): 395 – 413. 2023. Cited by: 0; All Open Access, Green Open Access

Paper doi link bibtex abstract

@ARTICLE{Yang2023395,
	author = {Yang, Qingjie and Zhou, Bing and Engsig, Marcus and Won, Moosoo and Riahi, Mohamed Kamel and Al-khaleel, Mohammad and Greenhalgh, Stewart},
	title = {Numerical Fréchet derivatives of the displacement tensor for 2.5-D frequency-domain seismic full-waveform inversion in viscoelastic TTI media},
	year = {2023},
	journal = {Near Surface Geophysics},
	volume = {21},
	number = {6},
	pages = {395 – 413},
	doi = {10.1002/nsg.12265},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85169698974&doi=10.1002%2fnsg.12265&partnerID=40&md5=3df4e2bc2291e2a655f8bdaa96013a47},
	abstract = {Derivatives of the displacement tensor with respect to the independent model parameters of the subsurface, also called Fréchet derivatives (or sensitivity kernels), are a key ingredient for seismic full-waveform inversion (FWI) with a local-search optimization algorithm. They provide a quantitative measure of the expected changes in the seismograms due to perturbations of the subsurface model parameters for a given survey geometry. Because 2.5-D wavefield modelling involves a real point source in a 2-D geological model with 3-D (spherical) wave properties, it yields synthetic data much closer to the actual practical field data than the commonly used 2-D wave simulation does, which uses an unrealistic line-source in which the waves spread cylindrically. Based on our recently developed general 2.5-D wavefield modelling scheme, we apply the perturbation method to obtain explicit analytic expressions for the derivatives of the displacement tensor for 2.5-D/2-D frequency-domain seismic FWI in general viscoelastic anisotropic media. We then demonstrate the numerical calculations of all these derivatives in two common cases: (1) viscoelastic isotropic; and (2) viscoelastic tilted transversely isotropic (TTI) solids. Examples of the differing sensitivity patterns for the various derivatives are investigated and compared for four different homogeneous models involving 2-D and 2.5-D modelling. Moreover, the numerical results are verified against the analytic solutions for homogeneous models. We further validate the numerical derivatives in a 2-D heterogeneous viscoelastic TTI case by conducting a synthetic data experiment of frequency-domain FWI to individually recover the 12 independent model parameters (density, dip angle, 5 elastic moduli and 5 corresponding Q-factors) in a simple model comprising an anomalous square box target embedded in a uniform background. Another 2.5-D multi-target model experiment presenting impacts from four common seismic surveying geometries validates the Fréchet derivatives again. © 2023 European Association of Geoscientists & Engineers.},
	note = {Cited by: 0; All Open Access, Green Open Access}
}

Derivatives of the displacement tensor with respect to the independent model parameters of the subsurface, also called Fréchet derivatives (or sensitivity kernels), are a key ingredient for seismic full-waveform inversion (FWI) with a local-search optimization algorithm. They provide a quantitative measure of the expected changes in the seismograms due to perturbations of the subsurface model parameters for a given survey geometry. Because 2.5-D wavefield modelling involves a real point source in a 2-D geological model with 3-D (spherical) wave properties, it yields synthetic data much closer to the actual practical field data than the commonly used 2-D wave simulation does, which uses an unrealistic line-source in which the waves spread cylindrically. Based on our recently developed general 2.5-D wavefield modelling scheme, we apply the perturbation method to obtain explicit analytic expressions for the derivatives of the displacement tensor for 2.5-D/2-D frequency-domain seismic FWI in general viscoelastic anisotropic media. We then demonstrate the numerical calculations of all these derivatives in two common cases: (1) viscoelastic isotropic; and (2) viscoelastic tilted transversely isotropic (TTI) solids. Examples of the differing sensitivity patterns for the various derivatives are investigated and compared for four different homogeneous models involving 2-D and 2.5-D modelling. Moreover, the numerical results are verified against the analytic solutions for homogeneous models. We further validate the numerical derivatives in a 2-D heterogeneous viscoelastic TTI case by conducting a synthetic data experiment of frequency-domain FWI to individually recover the 12 independent model parameters (density, dip angle, 5 elastic moduli and 5 corresponding Q-factors) in a simple model comprising an anomalous square box target embedded in a uniform background. Another 2.5-D multi-target model experiment presenting impacts from four common seismic surveying geometries validates the Fréchet derivatives again. © 2023 European Association of Geoscientists & Engineers.

Optimal Axial-Probe Design for Foucault-Current Tomography: A Global Optimization Approach Based on Linear Sampling Method. Benaissa, B.; Khatir, S.; Jouini, M. S.; and Riahi, M. K. Energies, 16(5). 2023. Cited by: 12; All Open Access, Gold Open Access

Optimal Axial-Probe Design for Foucault-Current Tomography: A Global Optimization Approach Based on Linear Sampling Method [link]

Paper doi link bibtex abstract

@ARTICLE{Benaissa2023,
	author = {Benaissa, Brahim and Khatir, Samir and Jouini, Mohamed Soufiane and Riahi, Mohamed Kamel},
	title = {Optimal Axial-Probe Design for Foucault-Current Tomography: A Global Optimization Approach Based on Linear Sampling Method},
	year = {2023},
	journal = {Energies},
	volume = {16},
	number = {5},
	doi = {10.3390/en16052448},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85149721564&doi=10.3390%2fen16052448&partnerID=40&md5=e3b9daab453951ab71e9e9fe0928f16f},
	abstract = {This paper is concerned with the optimal design of axial probes, commonly used in the Non-Destructive Testing (NDT) of tube boiling in steam generators. The goal is to improve the low-frequency Foucault-current imaging of these deposits by designing a novel probe. The approach uses a combination of an inverse problem solver with global optimization to find the optimal probe characteristics by minimizing a function of merit defined using image processing techniques. The evaluation of the function of merit is computationally intensive and a surrogate optimization approach is used, incorporating a multi-particle search algorithm. The proposed design is validated through numerical experiments and aims to improve the accuracy and efficiency of identifying deposits in steam generator tubes. © 2023 by the authors.},
	note = {Cited by: 12; All Open Access, Gold Open Access}
}

Improved ANN for Damage Identification in Laminated Composite Plate. Slimani, M.; Tiachacht, S.; Behtani, A.; Khatir, T.; Khatir, S.; Benaissa, B.; and Riahi, M. K. Lecture Notes in Civil Engineering, 317 LNCE: 186 – 198. 2023. Cited by: 5

Improved ANN for Damage Identification in Laminated Composite Plate [link]

Paper doi link bibtex abstract

@ARTICLE{Slimani2023186,
	author = {Slimani, Mohand and Tiachacht, Samir and Behtani, Amar and Khatir, Tawfiq and Khatir, Samir and Benaissa, Brahim and Riahi, Mohamed Kamel},
	title = {Improved ANN for Damage Identification in Laminated Composite Plate},
	year = {2023},
	journal = {Lecture Notes in Civil Engineering},
	volume = {317 LNCE},
	pages = {186 – 198},
	doi = {10.1007/978-3-031-24041-6_15},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85149808068&doi=10.1007%2f978-3-031-24041-6_15&partnerID=40&md5=fe3f0ef797f6e3b78b977febe40eea71},
	abstract = {This paper presents an improved Artificial Neural Network (ANN) for structural health monitoring of composite materials. Simply supported three-ply [0∘90∘0∘] square laminated plate modeled with a 9 × 9 grid is provided and validated based on the literature review. Modal strain energy change ratio (MSEcr) is used to localize the damaged elements and eliminate the healthy elements. Next, improved ANN using the Arithmetic optimization algorithm (AOA) used for structural quantification. AOA aims to optimize the parameters of ANN for better training. Several scenarios are considered to test the accuracy of the presented approach. The results showed that the approach can localize and quantify the damage correctly. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.},
	note = {Cited by: 5}
}

2022 (8)

Spectral Reconstruction of Magnetite Deposits in Steam Generator Tubing: An Artificial Intelligence Approach. Jouini, M. S.; and Riahi, M. K. In volume 127, pages 314-315, 2022.

Spectral Reconstruction of Magnetite Deposits in Steam Generator Tubing: An Artificial Intelligence Approach [link]

Paper link bibtex abstract

@inproceedings{,
	author = {Jouini, Mohamed Soufiane, and Riahi, Mohamed Kamel},
	title = {Spectral Reconstruction of Magnetite Deposits in Steam Generator Tubing: An Artificial Intelligence Approach},
	year = {2022},
	journal = {Transactions of the American Nuclear Society},
	volume = {127},
	pages = {314-315},
	number={1},
	doi = {},
	url = {https://www.ans.org/pubs/transactions/article-52359/},
	document_type={Article},
	abstract={Steam Generator (SG) tubing is a crucial component in
the Pressurized Water Reactors. A variety of degradation
of the SG tubes challenge the integrity of such component
and therefore the station reliability and even safety. Cracks,
hardening, stress corrosion are serious factors that threaten
tube failure, hence the safety of the power plant. To prevent
unwelcome radioactive accident, Non-Destructive Evaluation
(NDE) techniques are heavily used, among which tomography
by Eddy-Current (EC) excitation. The latter is considered
to be among the cheapest NDE techniques. In this work we
shall present a tomography inversion technique based on the
use of Artificial Intelligence (AI) together with Finite element
solution [1] to Eddy-current problem. A variety of inversion
technique have emerged, [2,3,4,5,6] and recently [7] without
being exhaustive. These techniques suffers from large memory
demand, and ill-posedness in the sense of dependency of the
output with respect to the initial guess. The latter method [7]
constitute a way around large memory requirement, although
it produces indicator function that is diffused hence not a clear
cut toward detecting the deposition. Nonetheless, the quality-
cost ratio for the LSM makes it highly potentially good method
to approximately detect conductive deposition and cracks. In
this work we aim at introducing AI technique as an alternative
approach for the NDE.}
}

Eddy-Current Tomographic Inversion Mathematical Tools for Non-Destructive Evaluation of Boiling Tubes. Haddar, H.; and Riahi, M. K. In volume 127, pages 426-427, 2022.

Eddy-Current Tomographic Inversion Mathematical Tools for Non-Destructive Evaluation of Boiling Tubes [link]

Paper link bibtex abstract

@inproceedings{riahi1ANSwinter2022,
	author = {Haddar, Houssem and Riahi, Mohamed Kamel},
	title = {Eddy-Current Tomographic Inversion Mathematical Tools for Non-Destructive Evaluation of Boiling Tubes},
	year = {2022},
	journal = {Transactions of the American Nuclear Society},
	volume = {127},
	pages = {426-427},
	number={1},
	doi = {},
	url = {https://www.ans.org/pubs/transactions/article-52386/},
	document_type={Article},
	abstract={Mechanical stress and corrosion modes represent the main
contributors to the degradation and fatigues of the steam gen-
erator (SG) tubing in nuclear power plants. The large variety
of the degradation types challenges the integrity and hence
the safety of the boiling tubes (BT) in the SG. The station
reliability remains highly sensitively dependent on the repairs
and replacement in the maintenance phase, which has recorded
an extensive activity worldwide in nuclear power plants sites
and stations. Novel technology tools beneficent from new
Mathematically developed algorithms play a key role in the
inspection and monitoring of tubes. This work aims at devel-
oping new efficient yet simple tool based on inverse problem
imaging to help in the Non-Destructive Evaluation (NDE) of
the BT. Our technique uses the Eddy-current excitation to im-
age the depositions of magnetite or possible cracks through
the newly developed Linear Sampling Method (LSM) [1],
which we couple with the variational based shape optimiza-
tion technique [2,3] to enhance the quality of the tomography
of depositions.}
}

PiTSBiCG: Parallel in time Stable Bi-Conjugate gradient algorithm. Riahi, M. K. Applied Numerical Mathematics, 181: 225-233. 2022.

PiTSBiCG: Parallel in time Stable Bi-Conjugate gradient algorithm [link]

Paper doi link bibtex abstract

@ARTICLE{Riahi2022225,
	author = {Riahi, Mohamed Kamel},
	title = {PiTSBiCG: Parallel in time Stable Bi-Conjugate gradient algorithm},
	year = {2022},
	journal = {Applied Numerical Mathematics},
	volume = {181},
	pages = {225-233},
	doi = {10.1016/j.apnum.2022.06.004},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85132505838&doi=10.1016%2fj.apnum.2022.06.004&partnerID=40&md5=5e9a3a3aae488c543249836121b90d4c},
author_keywords={Parallel in time algorithm, BiCGStab, parareal, Acceleration, Parallel computing,
Numerical Simulation of PDEs},document_type={Article},
abstract={This paper presents a new algorithm for the parallel in time (PiT) numerical simulation of time-dependent partial/ordinary differential equations. We propose a reliable alternative to the well
know parareal in time algorithm, by formulating the parallel in time problem algebraically and
solve it using an adapted Bi-Conjugate gradient stabilized method. The proposed Parallel in
time Stable Bi-Conjugate algorithm (PiTSBiCG) has great potential in stabilizing the parallel
resolution for a variety of problems. In this work, we describe the mathematical approach to the
new algorithm and provide numerical evidence that shows its superiority to the standard parareal
method.}
}

An efficient damage quantification based on Comprehensive learning Jaya algorithm in steel and composite structures. M Slimani, T K.; and Wahab, M A. Journal Structural Control and Health Monitoring, x(under review). 2022.

An efficient damage quantification based on Comprehensive learning Jaya algorithm in steel and composite structures [link]

Paper doi link bibtex abstract

@ARTICLE{Riahi2022-4,
author={M Slimani, T Khatir, S Tiachacht, S Khatir, B Benaissa , M. K. Riahi  and M Abdel Wahab},
title={An efficient damage quantification based on Comprehensive learning Jaya algorithm in steel and composite structures},
journal={Journal Structural Control and Health Monitoring},
year={2022},
volume={x},
number={under review},
doi={https://onlinelibrary.wiley.com/page/journal/15452263/homepage/productinformation.html},
art_number={},
url={https://onlinelibrary.wiley.com/page/journal/15452263/homepage/productinformation.html},
affiliation={Department of Applied Mathematics, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Emirates Nuclear Technology Center, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Nuclear Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Mechanical Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates},
abstract={This paper presents a structural health monitoring method based on the "normalized Modified Cornwell Indicator" (nMCI). An improved damage indicator in laminated composite structures, 2D truss structure, and 3D frame structure, for damage position and magnitude. The performance of the suggested approach is examined using innovative zero-order search algorithms, Namely E-Jaya, and the Comprehensive Learning Jaya Algorithm. Firstly, in cases of damage localization compared to the classical damage identification indicator, then in the study of damage quantification truss bridge and experimental modal analysis of Guangzhou TV Tower (China). The presented techniques are tested for single and multiple damages, including the convergence study and CPU time for better selection of good techniques. The robustness of the method is also examined against measurement uncertainty modeled as different levels of noise.},
author_keywords={},document_type={Article}
}

Dynamics of Non-Newtonian Tangent Hyperbolic Liquids Conveying Tiny Particles on Objects with Variable Thickness when Lorentz Force and Thermal Radiation are Significant. Nadeem, M.; Siddique, I.; Ali, R.; Riahi, M. K.; Mousa, A. A. A.; Khan, I.; Hafeez, H. M.; and Azam, M. Frontiers in Physics, 10. 2022.

Paper doi link bibtex abstract

@ARTICLE{10.3389/fphy.2022.917677,
AUTHOR={Nadeem, Muhammad and Siddique, Imran and Ali, Rifaqat and Riahi, Mohamed Kamel and Mousa, Abd Allah A. and Khan, Ilyas and Hafeez, Hafiza Mariyam and Azam, Muhammad},
TITLE={Dynamics of Non-Newtonian Tangent Hyperbolic Liquids Conveying Tiny Particles on Objects with Variable Thickness when Lorentz Force and Thermal Radiation are Significant},
JOURNAL={Frontiers in Physics},      
VOLUME={10},           
YEAR={2022},      
URL={https://www.frontiersin.org/articles/10.3389/fphy.2022.917677},       
DOI={10.3389/fphy.2022.917677},      
ISSN={2296-424X},
ABSTRACT={The flow via needle has prominent applications in the modern world such as nano-wires, microstructure electric gadgets, microsensors, surgical instruments and biological treatments. The present investigation focuses on boundary layer heat, flow, and mass transfer of MHD tangent hyperbolic fluid (conveying tiny particles) via a thin needle under the impacts of activation energy, non-constant thermal conductivity, heat source, and nonlinear thermal radiation. In the description of the Buongiorno model, the significant features of Brownian motion and thermophoresis have been included. Adopting appropriate transformations to the given problem specified by the set of partial differential equations yields the dimensionless form of ordinary differential equations After that, these obtained ODEs are solved numerically via MATLAB bvp4c. A comparative result with previous findings is conducted. Physical parametersÕ impact on flow rate, heat, and concentration is exhibited and explained in depth. The main findings of this study are that flow patterns reduce as the magnetic parameter and the Weissenberg number grow. Higher values of Brownian motion, heat source/sink, nonlinear radiation, and thermophoretic parameter improve the thermal profile. Moreover, the rate of heat transfer for the variable property case is significantly improved. Concentration profiles reduce as the thermophoresis parameter and chemical reaction parameter grow but improve as the activation energy and Brownian motion parameter rise. The percentage increase in Sherwood number is 35.07 and 5.44 when the thermophoresis takes input in the range 0 ² Nt ² 0.2 and activation energy parameters 0 ² E ² 0.2. The Weissenberg number and power-law index parameters are all designed to boost the Sherwood number.}
}

Analytic formula and validation of the Frechet derivatives for 2-D/2.5-D seismic full-waveform inversion in viscoelastic TTI media. Q. Yang, B. Z.; and Alkhaleel, M. PAAG. 2022.

Analytic formula and validation of the Frechet derivatives for 2-D/2.5-D seismic full-waveform inversion in viscoelastic TTI media [link]

Paper doi link bibtex abstract

@ARTICLE{Riahi2022-3,
author={Q. Yang, B. Zhou, M. K.Riahi and M. Alkhaleel},
title={Analytic formula and validation of the Frechet derivatives for 2-D/2.5-D seismic full-waveform inversion in viscoelastic TTI media},
journal={PAAG},
year={2022},
volume={},
number={},
doi={https://www.dropbox.com/s/1vkolxufh92lzvt/PAAG-D-21-00147_R2.pdf?dl=0},
art_number={},
url={https://www.dropbox.com/s/1vkolxufh92lzvt/PAAG-D-21-00147_R2.pdf?dl=0},
affiliation={Department of Applied Mathematics, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Emirates Nuclear Technology Center, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Nuclear Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Mechanical Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates},
abstract={The Frchet derivatives of the displacement vector with respect to the independent
parameter of the subsurface, also called sensitivity kernels, are the key ingredient for
the full-waveform inversion of seismic data. They quantitatively exhibit the sensitivity of
seismograms to perturbation of the subsurface model parameters and give the analytic
formula of the Jacobian matrix of seismic full-waveform data to all parameters of the
model. Because of using a real point source in a 2-D geological model (2.5-D) rather
than an unreal linear source, the 2.5-D wave modeling generates the synthetic data
more close to the practical data compared to the common 2-D wave simulation. In this
paper, we analytically deduce the explicit expressions of the Frchet derivatives for 2-
D/2.5-D frequency-domain seismic full-waveform inversion in viscoelastic anisotropic
media and demonstrate the numerical calculations of all the quantities of the Frchet
derivatives. Two common cases Ñ viscoelastic isotropic and viscoelastic tilted
transversely isotropic media are exhibited analytically. Four comparable 2-D and 2.5-D
examples are demonstrated numerically. Furthermore, we validate the Frchet
derivatives by carrying out the frequency-domain full-waveform inversion to individually
recover twelve model parameters (density, dipping angle, five independent moduli and
five corresponding quality factors) in a simple box model.},
author_keywords={Inverse problem, CI, nMCI, Convergence study, Damage quantification, Complex structures, Laminated composite, and noise},document_type={Article},
source={},
}

Recursive convolution method to solve the first-order viscoacoustic and viscoelastic wave equations. Chao Jin, B. Z.; and Moosoo Won, M. R. Geophysics, x(under review). 2022.

Recursive convolution method to solve the first-order viscoacoustic and viscoelastic wave equations [link]

Paper link bibtex abstract

@ARTICLE{Riahi2022-2,
author={Chao Jin, Bing Zhou, Moosoo Won, Mohamed Riahi, Mohamed Jamal Zemerly},
title={Recursive convolution method to solve the first-order
viscoacoustic and viscoelastic wave equations},
journal={Geophysics},
year={2022},
volume={x},
number={under review},
doi={},
art_number={},
url={},
affiliation={Department of Applied Mathematics, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Emirates Nuclear Technology Center, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Nuclear Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Mechanical Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates},
abstract={Seismic wave modeling in anelastic medium is a fundamental tool for seismic data processing
and interpretation in exploration geophysics. To compute the convolutions in the constitutive
equation of an anelastic medium, we propose a new semi-analytical method, called the Ôrecursive
convolution methodÕ to replace solving the auxiliary partial differential equations of the memory
variables. New sets of the first-order viscoacoustic and viscoelastic wave equations in the time
domain are established, and show the new method does not require solving the auxiliary partial
different equations of the memory variables like the traditional methods do. The new method
may accurately simulate the viscoacoustic and viscoelastic waves with a standard grid finite
difference method without any additional computational costs compared to the traditional
method, and its accuracy may reach the satisfactory levels as a high-order time-stepping formula
and the staggered grid are applied to the traditional method. Our numerical experiments verify
the feasibility and accuracy of the new method to solve the first-order viscoacoustic and
viscoelastic wave equations, as well as the validation of the staggered grid finite-difference
method.},
author_keywords={},document_type={Article}
}

%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Combined Newton-Raphson and Streamlines-Upwind Petrov-Galerkin iterations for nanoparticles transport in buoyancy-driven flow. Riahi, M.; Ali, M.; Addad, Y.; and Abu-Nada, E. Journal of Engineering Mathematics, 132(1). 2022.

Combined Newton-Raphson and Streamlines-Upwind Petrov-Galerkin iterations for nanoparticles transport in buoyancy-driven flow [link]

Paper doi link bibtex abstract

@ARTICLE{Riahi2022,
author={Riahi, M.K. and Ali, M. and Addad, Y. and Abu-Nada, E.},
title={Combined Newton-Raphson and Streamlines-Upwind Petrov-Galerkin iterations for nanoparticles transport in buoyancy-driven flow},
journal={Journal of Engineering Mathematics},
year={2022},
volume={132},
number={1},
doi={10.1007/s10665-021-10205-4},
art_number={22},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85123031898&doi=10.1007%2fs10665-021-10205-4&partnerID=40&md5=47681d80babdff9ff79a672932990c0f},
affiliation={Department of Applied Mathematics, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Emirates Nuclear Technology Center, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Nuclear Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Mechanical Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates},
abstract={The present study deals with the finite element discretization of nanofluid convective transport in an enclosure with variable properties. We study the Buongiorno model, which couples the NavierÐStokes equations for the base fluid, an advective-diffusion equation for the heat transfer, and an advection-dominated nanoparticle fraction concentration subject to thermophoresis and Brownian motion forces. We develop an iterative numerical scheme that combines NewtonÕs method (dedicated to the resolution of the momentum and energy equations) with the transport equation that governs the nanoparticles concentration in the enclosure. We show that the Stream-Upwind PetrovÐGalerkin regularization approach is required to solve properly the transport equation in BuongiornoÕs model, in the Finite Element framework. Indeed, we formulate this ill-posed equation as a variational problem under mean value constraint. Numerical analysis and computations are reported to show the effectiveness of our proposed numerical approach in its ability to provide reasonably good agreement with the experimental results available in the literature. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.},
author_keywords={Advection-dominated equation;  Finite element method;  Nanofluid;  Nanofluid heat transfer;  NavierÐStokes equations;  NewtonÐRaphson method;  Stream-Upwind PetrovÐGalerkin},
document_type={Article}
}

2021 (5)

Frequency-domain seismic data transformation from point-source to line-source for 2D viscoelastic anisotropic media. Yang, Q.; Zhou, B.; Riahi, M.; and Al-Khaleel, M. Geophysics, 87(2). 2021.

Frequency-domain seismic data transformation from point-source to line-source for 2D viscoelastic anisotropic media [link]

Paper doi link bibtex abstract

@ARTICLE{Yang2021,
author={Yang, Q. and Zhou, B. and Riahi, M.K. and Al-Khaleel, M.},
title={Frequency-domain seismic data transformation from point-source to line-source for 2D viscoelastic anisotropic media},
journal={Geophysics},
year={2021},
volume={87},
number={2},
doi={10.1190/geo2021-0166.1},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85121218666&doi=10.1190%2fgeo2021-0166.1&partnerID=40&md5=08fcab005be8bec0f96a1e589363831a},
affiliation={Khalifa University of Science and Technology, Department of Earth Science, Abu Dhabi, United Arab Emirates; Khalifa University of Science and Technology, Department of Applied Mathematics, Abu Dhabi, 46668, United Arab Emirates},
abstract={We present a simple yet effective transform function to convert 3D point-source seismic data to equivalent 2D line-source data, which is required when applying efficient 2D migration and full-waveform inversion to field data collected along a line. By numerically comparing the 3D and corresponding 2D Greenå's tensors in various media, the phase shift around 45¡ and the offset amplitude compensation factor, as well as small fluctuations of the amplitude ratios are observed in all nonzero components of the wave-equation solutions. Based on these observations, we derive a transform function comprised of (1) a simple filter for compensating amplitude and phase shift, and (2) stretching scalars for scaling amplitude differences for different components. We employ the 3D and 2D analytical wave solutions in various homogeneous media to demonstrate the accuracy of the proposed transform function, and then apply it to a heterogeneous, viscoelastic, anisotropic model and a modified Marmousi model. All of these results indicate that the proposed transform function is applicable for the conversion of point-source data to equivalent line-source data for imaging 2D subsurface structure. © 2022 Society of Exploration Geophysicists.},
author_keywords={frequency-domain;  signal processing;  wave propagation},
document_type={Article}
}

Numerical investigation of nanoparticles slip mechanisms impact on the natural convection heat transfer characteristics of nanofluids in an enclosure. Amidu, M.; Addad, Y.; Riahi, M.; and Abu-Nada, E. Scientific Reports, 11(1). 2021.

Paper doi link bibtex abstract

@ARTICLE{Amidu2021,
author={Amidu, M.A. and Addad, Y. and Riahi, M.K. and Abu-Nada, E.},
title={Numerical investigation of nanoparticles slip mechanisms impact on the natural convection heat transfer characteristics of nanofluids in an enclosure},
journal={Scientific Reports},
year={2021},
volume={11},
number={1},
doi={10.1038/s41598-021-95269-z},
art_number={15678},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85112011779&doi=10.1038%2fs41598-021-95269-z&partnerID=40&md5=e8b02a920041deb3aa95f14834047590},
affiliation={Department of Nuclear Engineering, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates; Emirates Nuclear Technology Center (ENTC), Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates; Department of Mathematics, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates; Department of Mechanical Engineering, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates},
abstract={This study intends to give qualitative results toward the understanding of different slip mechanisms impact on the natural heat transfer performance of nanofluids. The slip mechanisms considered in this study are Brownian diffusion, thermophoretic diffusion, and sedimentation. This study compares three different Eulerian nanofluid models; Single-phase, two-phase, and a third model that consists of incorporating the three slip mechanisms in a two-phase drift-flux. These slip mechanisms are found to have different impacts depending on the nanoparticle concentration, where this effect ranges from negligible to dominant. It has been reported experimentally in the literature that, with high nanoparticle volume fraction the heat transfer deteriorates. Admittingly, classical nanofluid models are known to underpredict this impairment. To address this discrepancy, this study focuses on the effect of thermophoretic diffusion and sedimentation outcome as these two mechanisms turn out to be influencing players in the resulting heat transfer rate using the two-phase model. In particular, the necessity to account for the sedimentation contribution toward qualitative modeling of the heat transfer is highlighted. To this end, correlations relating the thermophoretic and sedimentation coefficients to the nanofluid concentration and Rayleigh number are proposed in this study. Numerical experiments are presented to show the effectiveness of the proposed two-phase model in approaching the experimental data, for the full range of Rayleigh number in the laminar flow regime and for nanoparticles concentration of (0% to 3%), with great satisfaction. © 2021, The Author(s).},
document_type={Article}
}

YUKI Algorithm and POD-RBF for Elastostatic and dynamic crack identification. Benaissa, B.; Hocine, N.; Khatir, S.; Riahi, M.; and Mirjalili, S. Journal of Computational Science, 55. 2021.

YUKI Algorithm and POD-RBF for Elastostatic and dynamic crack identification [link]

Paper doi link bibtex abstract

@ARTICLE{Benaissa2021,
author={Benaissa, B. and Hocine, N.A. and Khatir, S. and Riahi, M.K. and Mirjalili, S.},
title={YUKI Algorithm and POD-RBF for Elastostatic and dynamic crack identification},
journal={Journal of Computational Science},
year={2021},
volume={55},
doi={10.1016/j.jocs.2021.101451},
art_number={101451},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85116494164&doi=10.1016%2fj.jocs.2021.101451&partnerID=40&md5=f93d2a200718442024311432e5643b8a},
affiliation={Toyota Technological Institute, Department of Mechanical Systems Engineering, Design Engineering Lab, 468-8511 Aichi, Nagoya, Tempaku Ward, Hisakata, 2 Chome-12-1, Japan; INSA CVL, Univ. Tours, Univ. Orlans, LaM, 3 rue de la Chocolaterie, Blois, Cedex, CS 23410, 41034, France; Soete Laboratory, Faculty of Engineering and Architecture, Ghent University, Technologiepark Zwijnaarde 903, Zwijnaarde, B-9052, Belgium; Faculty of Civil Engineering, Ho Chi Minh City Open University, Ho Chi Minh City, Viet Nam; Department of Mathematics, Khalifa University of Sciences and Technology, P.O. Box 127788, Abu Dhabi, United Arab Emirates; Emirates Nuclear Technology Center (ENTC), Khalifa University of Science and Technology, United Arab Emirates; Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Fortitude Valley, Brisbane, QLD, 4006, Australia; Yonsei Frontier Lab, Yonsei University, Seoul, South Korea},
abstract={This paper proposes a new metaheuristic algorithm with a search space reduction capability guided by simple formalism. The search population focuses partially on the inside the local search area while the rest explore globally, looking for better search areas. We call the new algorithm by YUKI Algoritm (YA) and employ it in a crack identification problem. With the aid of a set of measurements taken on the defected structure, we aim at identifying the crack parameters such as length and orientation. To this end, we use the so-called model reduction technique through Proper orthogonal Decomposition (POD) endorsed with Radial Basic Function (RBF), which helps in predicting (numerically) the measurement at new points (out of the set of sensors) via interpolation. This method is widely used in this context and was proven very effective computational-wise. In our study of the performance of YA, we deal with two cases; Firstly, in the case of the Elastostatic study. And secondly, in the case of dynamic analysis. We compare the performance of the suggested algorithm with the performance of well-known optimization methods, such as Teaching Learning Based Optimization (TLBO), Cuckoo Search (CS), and the Gray Wolf Optimizer (GWO). The results show that YA provides accurate and faster results compared to the mentioned algorithms. © 2021 Elsevier B.V.},
author_keywords={Crack identification;  Inverse problem;  POD-RBF;  Static and dynamic analysis;  Yuki Algorithm},
document_type={Article}

}

Near-field linear sampling method for axisymmetric eddy current tomography. Haddar, H.; and Riahi, M. Inverse Problems, 37(10). 2021.

Near-field linear sampling method for axisymmetric eddy current tomography [link]

Paper doi link bibtex abstract

@ARTICLE{Haddar2021,
author={Haddar, H. and Riahi, M.K.},
title={Near-field linear sampling method for axisymmetric eddy current tomography},
journal={Inverse Problems},
year={2021},
volume={37},
number={10},
doi={10.1088/1361-6420/ac1c50},
art_number={105002},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85115133176&doi=10.1088%2f1361-6420%2fac1c50&partnerID=40&md5=cb8471176dcfcb6181fbb62912b8607f},
affiliation={INRIA, Ecole Polytechnique (CMAP), Universit Saclay Ile de France, Route de Saclay, Palaiseau, 91128, France; Department of Mathematics, Khalifa University of Sciences and Technology, P.O. Box 127788, Abu Dhabi, United Arab Emirates; Emirates Nuclear Technology Center (ENTC), Khalifa University of Science and Technology, United Arab Emirates},
abstract={This paper is concerned with eddy-current (EC) nondestructive testing of conductive materials and focuses, in particular, on extending the well-known linear sampling method (LSM) to the case of EC equations. We first present the theoretical foundation of the LSM in the present context and in the case of point sources. We then explain how this method can be adapted to a realistic setting of EC probes. In the case of identifying the shape of external deposits from impedance measurements taken from inside of the tube (steam generator), we show how the method can be applied to measurements obtained from a sweeping set of coils. Numerical experiments suggest that good results can be achieved using only a few coils and even in the limiting case of backscattering data. © 2021 IOP Publishing Ltd.},
author_keywords={eddy-current;  impedance measurement;  inverse imaging;  linear sampling method;  non destructivetesting;  tomography of deposits},
document_type={Article}

}

On the convergence rate of Fletcher-Reeves nonlinear conjugate gradient methods satisfying strong Wolfe conditions: Application to parameter identification in problems governed by general dynamics. Riahi, M.; and Qattan, I. Mathematical Methods in the Applied Sciences. 2021.

Paper doi link bibtex abstract

@ARTICLE{Riahi2021,
author={Riahi, M.K. and Qattan, I.A.},
title={On the convergence rate of Fletcher-Reeves nonlinear conjugate gradient methods satisfying strong Wolfe conditions: Application to parameter identification in problems governed by general dynamics},
journal={Mathematical Methods in the Applied Sciences},
year={2021},
doi={10.1002/mma.8009},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85121447037&doi=10.1002%2fmma.8009&partnerID=40&md5=a407f638c2faf5bee880676835703471},
affiliation={Department of Mathematics, Khalifa University of Sciences and Technology, Abu Dhabi, United Arab Emirates; Department of Physics, Khalifa University of Sciences and Technology, Abu Dhabi, United Arab Emirates},
abstract={Over the last decades, many efforts have been made toward the understanding of the convergence rate of the gradient-based method for both constrained and unconstrained optimization. The cases of the strongly convex and weakly convex payoff function have been extensively studied and are nowadays fully understood. Despite the impressive advances made in the convex optimization context, the nonlinear non-convex optimization problems are still not fully exploited. In this paper, we are concerned with the nonlinear, non-convex optimization problem under system dynamic constraints. We apply our analysis to parameter identification of systems governed by general nonlinear differential equations. The considered inverse problem is presented using optimal control tools. We tackle the optimization through the use of Fletcher-Reeves nonlinear conjugate gradient method satisfying strong Wolfe conditions with inexact line search. We rigorously establish a convergence analysis of the method and report a new linear convergence rate which forms the main contribution of this work. The theoretical result reported in our analysis requires that the second derivative of the payoff functional be continuous and bounded. Numerical evidence on a selection of popular nonlinear models is presented as a direct application of parameter identification to support the theoretical findings. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.},
author_keywords={convergence analysis;  dynamical systems;  inverse problem;  nonlinear conjugate gradient methods;  nonlinear optimal control;  parameter identification},
document_type={Article}
}

2020 (6)

A new generalized stiffness reduction method for 2D/2.5D frequency-domain seismic wave modeling in viscoelastic anisotropic media. Yang, Q.; Zhou, B.; Riahi, M.; and Al-Khaleel, M. Geophysics, 85(6): T315-T329. 2020.

A new generalized stiffness reduction method for 2D/2.5D frequency-domain seismic wave modeling in viscoelastic anisotropic media [link]

Paper doi link bibtex abstract

@ARTICLE{Yang2020T315,
author={Yang, Q. and Zhou, B. and Riahi, M.K. and Al-Khaleel, M.},
title={A new generalized stiffness reduction method for 2D/2.5D frequency-domain seismic wave modeling in viscoelastic anisotropic media},
journal={Geophysics},
year={2020},
volume={85},
number={6},
pages={T315-T329},
doi={10.1190/GEO2020-0143.1},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85100948478&doi=10.1190%2fGEO2020-0143.1&partnerID=40&md5=9478205ff4d9586ba86a7e8feef3f40c},
affiliation={Khalifa University of Science and Technology, Department of Earth Science, Abu Dhabi, 127788, United Arab Emirates; Khalifa University of Science and Technology, Department of Applied Mathematics, Abu Dhabi, 127788, United Arab Emirates; Khalifa University, Department of Applied Mathematics, Abu Dhabi, 127788, United Arab Emirates; Yarmouk University, Mathematics Department, Irbid, 21163, Jordan},
abstract={In frequency-domain seismic wave modeling, absorbing artificial reflections is crucial to obtain accurate numerical solutions. We have determined that, in viscoelastic anisotropic media (VEAM), the most popular absorbing boundary techniques, such as the perfectly matched layer and the generalized stiffness reduction method (GSRM), fail. Then, we develop a new version of the GSRM and incorporate it into a 2D/2.5D spectral element method. We find with extensive nontrivial numerical experiments that the new GSRM exhibits excellent features of simple and efficient implementation, while handling free-surface and subsurface interface topography. Furthermore, we find that sampling the positive wavenumber range is an efficient strategy to compute the 3D wavefield in arbitrary 2D VEAM, and the new version takes full advantage of the symmetry/antisymmetry of the wavefield. The new GSRM removes artificial reflections by damping the real and imaginary viscoelastic moduli in different ways. The wavefields in two vertically transverse isotropic and one orthorhombic viscoelastic homogeneous models are compared with the corresponding analytical solutions to show the high accuracy performance of the new GSRM. Finally, a complex 2D geologic model with irregular free-surface and subinterface is considered to present the modeling technique and its adaptation capacity for complex 2D VEAM. © 2020 Society of Exploration Geophysicists. All rights reserved.},
document_type={Article},

}

A hybrid multiphase flow model for the prediction of both low and high void fraction nucleate boiling regimes. Amidu, M.; Addad, Y.; and Riahi, M. Applied Thermal Engineering, 178. 2020.
$A hybrid multiphase flow model for the prediction of both low and high void fraction nucleate boiling regimes [link]$ Paper doi link bibtex

@ARTICLE{Amidu2020,
author={Amidu, M.A. and Addad, Y. and Riahi, M.K.},
title={A hybrid multiphase flow model for the prediction of both low and high void fraction nucleate boiling regimes},
journal={Applied Thermal Engineering},
year={2020},
volume={178},
doi={10.1016/j.applthermaleng.2020.115625},
art_number={115625},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087319857&doi=10.1016%2fj.applthermaleng.2020.115625&partnerID=40&md5=51ab79dd2941e8f226a5f4dabec1849c},
document_type={Article},

}

CSIOR: Circle-Surface Intersection Ordered Resampling. Tortorici, C.; Riahi, M.; Berretti, S.; and Werghi, N. Computer Aided Geometric Design, 79. 2020.

CSIOR: Circle-Surface Intersection Ordered Resampling [link]

Paper doi link bibtex

@ARTICLE{Tortorici2020,
author={Tortorici, C. and Riahi, M.K. and Berretti, S. and Werghi, N.},
title={CSIOR: Circle-Surface Intersection Ordered Resampling},
journal={Computer Aided Geometric Design},
year={2020},
volume={79},
doi={10.1016/j.cagd.2020.101837},
art_number={101837},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85083215012&doi=10.1016%2fj.cagd.2020.101837&partnerID=40&md5=691e7f69b3beb7cd4292bcaccc28d9d8},
document_type={Article},

}

CSIOR: An ordered structured resampling of mesh surfaces. Tortorici, C.; Riahi, M.; Berretti, S.; and Werghi, N. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 12015 LNCS: 28-41. 2020.

CSIOR: An ordered structured resampling of mesh surfaces [link]

Paper doi link bibtex

@ARTICLE{Tortorici202028,
author={Tortorici, C. and Riahi, M. and Berretti, S. and Werghi, N.},
title={CSIOR: An ordered structured resampling of mesh surfaces},
journal={Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
year={2020},
volume={12015 LNCS},
pages={28-41},
doi={10.1007/978-3-030-54407-2_3},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85089607666&doi=10.1007%2f978-3-030-54407-2_3&partnerID=40&md5=18053a0f5534f2053e169b0bf5784d62},
document_type={Conference Paper},

}

An effective numerical method to remove the edge effects for seismic wave modeling in arbitrary viscoelastic anisotropic media. Yang, Q.; Zhou, B.; Riahi, M.; and Al-Khaleel, M. 2020.

An effective numerical method to remove the edge effects for seismic wave modeling in arbitrary viscoelastic anisotropic media [link]

Paper doi link bibtex abstract

@CONFERENCE{Yang20202704,
author={Yang, Q. and Zhou, B. and Riahi, M.K. and Al-Khaleel, M.},
title={An effective numerical method to remove the edge effects for seismic wave modeling in arbitrary viscoelastic anisotropic media},
journal={SEG Technical Program Expanded Abstracts},
year={2020},
volume={2020-October},
pages={2704-2708},
doi={10.1190/segam2020-3410414.1},
art_number={2851},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85119057233&doi=10.1190%2fsegam2020-3410414.1&partnerID=40&md5=fb65e597b80fa2c35397881d45434d3c},
affiliation={Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates},
abstract={The generalized stiffness reduction method (GSRM) was previously proposed to absorb the artificial reflections in seismic wave modeling in arbitrary elastic anisotropic media. However, the traditional PML technique and the original GSRM lose their effectiveness of removing the artificial edge effects in viscoelastic anisotropic media. To overcome this issue, we propose a new version of the GSRM to attenuate the viscoelastic waves arriving the edges of the grid. The frequency-domain wave modeling is carried out in VTI media and shows the results used the PML and two GSRMs. Comparing the numerical solutions with the analytic solutions, we show perfect matchings of the wavefields by using the new version of the GSRM comparing to the use of the PML and the original GSRM, which exhibit serious deviations from the true solution. Moreover, the new version of the GSRM maintains the simple numerical implementation of the original GRSM. © 2020 Society of Exploration Geophysicists.},
author_keywords={Attenuation;  Boundary conditions;  Modeling;  Viscoelastic},
document_type={Conference Paper},

}

Failures of the perfectly-matched layer method in frequency-domain seismic wave modelling in elastic anisotropic media. Zhou, B.; Greenhalgh, S.; Liu, X.; Bouzidi, Y.; Riahi, M.; and Al-Khaleel, M. 2020.

Failures of the perfectly-matched layer method in frequency-domain seismic wave modelling in elastic anisotropic media [link]

Paper doi link bibtex abstract

@CONFERENCE{Zhou20203750,
author={Zhou, B. and Greenhalgh, S. and Liu, X. and Bouzidi, Y. and Riahi, M.K. and Al-Khaleel, M.},
title={Failures of the perfectly-matched layer method in frequency-domain seismic wave modelling in elastic anisotropic media},
journal={SEG International Exposition and Annual Meeting 2019},
year={2020},
pages={3750-3754},
doi={10.1190/segam2019-3209086.1},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85079494065&doi=10.1190%2fsegam2019-3209086.1&partnerID=40&md5=c8ebed28340e20acbeb52b3891a5815c},
affiliation={College of Art and Sciences, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates; CPG, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia},
abstract={The perfectly-matched layer (PML) technique is popular approach to remove the artificial edge effects in numerical wave modelling. However, there are stability conditions of the PML which all wavefronts must satisfy, such as the spherical wavefronts of P and S waves in elastic isotropic media. But the qSV wavefronts in anisotropic media may present severe instability of the PML because of triplications or cusps. In this paper, we give examples showing the failures of the PML in frequency-domain seismic wave modelling and how serious the problem can be. Our results demonstrate that the frequency-domain wave solutions may be destroyed by intersecting qSV wavefronts in singular directions. To overcome this issue, we introduce a generalized stiffness reduction method (GSRM) that aims at stabilizing the absorbing layer. We show that the GSRM successfully dissipates the wave energy to such an extent at the edge of the grid so that the spurious boundary reflections are minimized. Our numerical examples prove that the GSRM can replace the PML in frequency-domain seismic wave modelling in arbitrary elastic anisotropic media. © 2019 SEG},
document_type={Conference Paper},

}

2019 (4)

. Zhou, B.; Greenhalgh, S.; Liu, X.; Bouzidi, Y.; Riahi, M. K.; and Al-Khaleel, M. Failures of the perfectly-matched layer method in frequency-domain seismic wave modelling in elastic anisotropic media, pages 3750-3754. 2019.

Paper doi link bibtex abstract

@inbook{doi:10.1190/segam2019-3209086.1,
author = {Bing Zhou and Stewart Greenhalgh and Xu Liu and Youcef Bouzidi and Mohamed Kamel Riahi and Mohammad Al-Khaleel},
title = {Failures of the perfectly-matched layer method in frequency-domain seismic wave modelling in elastic anisotropic media},
booktitle = {SEG Technical Program Expanded Abstracts 2019},
chapter = {},
pages = {3750-3754},
year = {2019},
doi = {10.1190/segam2019-3209086.1},
URL = {https://library.seg.org/doi/abs/10.1190/segam2019-3209086.1},
eprint = {https://library.seg.org/doi/pdf/10.1190/segam2019-3209086.1},
    abstract = { The perfectly-matched layer (PML) technique is popular approach to remove the artificial edge effects in numerical wave modelling. However, there are stability conditions of the PML which all wavefronts must satisfy, such as the spherical wavefronts of P and S waves in elastic isotropic media. But the qSV wavefronts in anisotropic media may present severe instability of the PML because of triplications or cusps. In this paper, we give examples showing the failures of the PML in frequency-domain seismic wave modelling and how serious the problem can be. Our results demonstrate that the frequency-domain wave solutions may be destroyed by intersecting qSV wavefronts in singular directions. To overcome this issue, we introduce a generalized stiffness reduction method (GSRM) that aims at stabilizing the absorbing layer. We show that the GSRM successfully dissipates the wave energy to such an extent at the edge of the grid so that the spurious boundary reflections are minimized. Our numerical examples prove that the GSRM can replace the PML in frequency-domain seismic wave modelling in arbitrary elastic anisotropic media.Presentation Date: Monday, September 16, 2019Session Start Time: 1:50 PMPresentation Start Time: 2:40 PMLocation: 304APresentation Type: Oral }
}

Dielectrophoresis Multipath Focusing of Microparticles through Perforated Electrodes in Microfluidic Channels. Alazzam, A.; Al-Khaleel, M.; Riahi, M. K.; Mathew, B.; Gawanmeh, A.; and Nerguizian, V. Biosensors, 9(3). 2019.

Dielectrophoresis Multipath Focusing of Microparticles through Perforated Electrodes in Microfluidic Channels [link]

Paper doi link bibtex abstract

@Article{bios9030099,
AUTHOR = {Alazzam, Anas and Al-Khaleel, Mohammad and Riahi, Mohamed Kamel and Mathew, Bobby and Gawanmeh, Amjad and Nerguizian, VahÃ©},
TITLE = {Dielectrophoresis Multipath Focusing of Microparticles through Perforated Electrodes in Microfluidic Channels},
JOURNAL = {Biosensors},
VOLUME = {9},
YEAR = {2019},
NUMBER = {3},
ARTICLE-NUMBER = {99},
URL = {https://www.mdpi.com/2079-6374/9/3/99},
ISSN = {2079-6374},
ABSTRACT = {This paper presents focusing of microparticles in multiple paths within the direction of the flow using dielectrophoresis. The focusing of microparticles is realized through partially perforated electrodes within the microchannel. A continuous electrode on the top surface of the microchannel is considered, while the bottom side is made of a circular meshed perforated electrode. For the mathematical model of this microfluidic channel, inertia, buoyancy, drag and dielectrophoretic forces are brought up in the motion equation of the microparticles. The dielectrophoretic force is accounted for through a finite element discretization taking into account the perforated 3D geometry within the microchannel. An ordinary differential equation is solved to track the trajectories of the microparticles. For the case of continuous electrodes using the same mathematical model, the numerical simulation shows a very good agreement with the experiments, and this confirms the validation of focusing of microparticles within the proposed perforated electrode microchannel. Microparticles of silicon dioxide and polystyrene are used for this analysis. Their initial positions and radius, the Reynolds number, and the radius of the pore in perforated electrodes mainly conduct microparticles trajectories. Moreover, the radius of the pore of perforated electrode is the dominant factor in the steady state levitation height.},
DOI = {10.3390/bios9030099}
}

Identifying short-and long-time modes of the mean-square displacement: An improved nonlinear fitting approach. Riahi, M.; Qattan, I.; Hassan, J; and Homouz, D AIP Advances, 9(5): 055112. 2019.
doi link bibtex abstract

@article{riahi2019identifying,
abstract = {This paper is concerned with fitting the mean-square displacement (MSD) function, and extract reliable and accurate values for the diffusion coefficient ??. In this work, we present a new optimal and robust nonlinear regression model capable of fitting the MSD function with different regimes corresponding to different time scales. The algorithm presented here achieves two major goals; a more accurate estimation of ?? as well as extracting information about the short time behavior. The algorithm fits the MSD to a continuous piece-wise function and predicts all the coefficients in the model including the breakpoints. The novelty of this approach lies in its ability to find the breakpoints which separate different modes of motion. We tested our algorithm using numerical experiments, and our fits described the data remarkably well. In addition, we applied our algorithm to extract ?? for water based on Molecular Dynamics (MD) simulations. The results of our fits are in good agreement with the experimentally reported values.},
  title={Identifying short-and long-time modes of the mean-square displacement: An improved nonlinear fitting approach},
  author={Riahi, MK and Qattan, IA and Hassan, J and Homouz, D},
  journal={AIP Advances},
  volume={9},
  number={5},
  pages={055112},
  year={2019},
  doi = {https://doi.org/10.1063/1.5098051},
  issn = {2158-3226},
  publisher={AIP Publishing}
}

A NEW LINEAR CONVERGENCE RATE FOR NONLINEAR CONJUGATE GRADIENT METHODS FOR PARAMETER IDENTIFICATION IN PROBLEMS GOVERNED BY GENERAL DIFFERENTIAL EQUATIONS. Riahi, M K; and Qattan, I A Appl. Comput. Math. (submitted). 2019.

Paper link bibtex abstract

@article{preprint,
abstract = {This paper presents a general description of a parameter estimation inverse prob- lem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the minimization process is based on a first-order optimization technique such as adaptive monotony-backtracking steepest descent technique and nonlinear conjugate gradient methods satisfying strong Wolfe conditions. Global convergence theory of both methods is rigorously established where new linear convergence rates are reported. Indeed, for the nonlinear non-convex optimization we show that under the Lipschitz-continuous condition of the gradient of the objective function we have a linear con- vergence rate toward a stationary point. Furthermore, nonlinear conjugate gradient method is shown to be linearly convergent toward stationary points where the second derivative of the ob- jective function is bounded. The convergence analysis in this work has been established in a general nonlinear non-convex optimization under constraints framework where the considered time-dependent model could be a system of coupled ordinary differential equations or partial dif- ferential equations. Numerical evidence on a selection of popular nonlinear models is presented to support the theoretical results.},
author = {Riahi, M K and Qattan, I A},
journal = {Appl. Comput. Math. (submitted)},
keywords = {Convergence analysis,Dynamical systems,Nonlinear Conjugate gradient methods,Nonlinear Optimal control,Parameter estimation and Inverse problem},
title = {{A NEW LINEAR CONVERGENCE RATE FOR NONLINEAR CONJUGATE GRADIENT METHODS FOR PARAMETER IDENTIFICATION IN PROBLEMS GOVERNED BY GENERAL DIFFERENTIAL EQUATIONS}},
url = {https://arxiv.org/abs/1806.10197},
year = {2019}
}

2018 (2)

Magnetohydrodynamic in partially heated square cavity with variable properties: Discrepancy in experimental and theoretical conductivity correlations. Astanina, M. S.; Kamel Riahi, M.; Abu-Nada, E.; and Sheremet, M. A. International Journal of Heat and Mass Transfer, 116: 532–548. 2018.
doi link bibtex abstract

@article{Astanina2018,
abstract = {Natural convection nanofluid heat transfer enhancement in a partially heated cavity is considered under the effect of an external Lorentz force exerted through interaction of the nanoparticles and the applied constant magnetic field. The aluminum oxide (Al2O3or alumina) nanofluid is considered to be with variable properties (i.e. thermal conductivity, viscosity and electric conductivity) and the cavity is partially heated from its left top corner. The effect of the inclination angle of the applied magnetic field is studied and analyzed. The Nusselt number is calculated at the heater to probe the heat transfer enhancement. Both effective thermal and electric conductivities have been investigated in their respective theoretical and experimental correlations. Numerical experiments are presented to show the discrepancy in heat transfer with the use of such correlations. A substantial difference in the heat transfer is noticed for the use of different correlations. An adverse effect is identified and analyzed with the increase of Hartmann number, the nanoparticle volume fraction, and the position of the heater within the cavity.},
author = {Astanina, Marina S. and {Kamel Riahi}, Mohamed and Abu-Nada, Eiyad and Sheremet, Mikhail A.},
doi = {10.1016/j.ijheatmasstransfer.2017.09.050},
issn = {00179310},
journal = {International Journal of Heat and Mass Transfer},
keywords = {Heat transfer enhancement,Magnetohydrodynamics,Nanofluid,Natural convection,Variable properties},
pages = {532--548},
title = {{Magnetohydrodynamic in partially heated square cavity with variable properties: Discrepancy in experimental and theoretical conductivity correlations}},
volume = {116},
year = {2018}
}

Improved extraction of two-photon exchange amplitudes from elastic electron-proton scattering cross section data up to Q2=5.20 (GeV/ c)2. Qattan, I. A.; Homouz, D.; and Riahi, M. K. Physical Review C, 97(4). 2018.
doi link bibtex abstract

@article{Qattan2018,
abstract = {{\textcopyright} 2018 American Physical Society. In this work, we improve on and extend to low- and high-Q2 values the extractions of the two-photon-exchange (TPE) amplitudes and the ratio Pl/PlBorn(Ïµ,Q2) using world data on electron-proton elastic scattering cross section $\sigma$R(Ïµ,Q2) with an emphasis on data covering the high-momentum region, up to Q2=5.20(GeV/c)2, to better constrain the TPE amplitudes in this region. We provide a new parametrization of the TPE amplitudes, along with an estimate of the fit uncertainties. We compare the results to several previous phenomenological extractions and hadronic TPE predictions. We use the new parametrization of the TPE amplitudes to extract the ratio Pl/PlBorn(Ïµ,Q2), and then compare the results to previous extractions, several theoretical calculations, and direct measurements at Q2=2.50(GeV/c)2.},
author = {Qattan, I. A. and Homouz, D. and Riahi, M. K.},
doi = {10.1103/PhysRevC.97.045201},
issn = {24699993},
journal = {Physical Review C},
number = {4},
title = {{Improved extraction of two-photon exchange amplitudes from elastic electron-proton scattering cross section data up to Q2=5.20 (GeV/ c)2}},
volume = {97},
year = {2018}
}

© 2018 American Physical Society. In this work, we improve on and extend to low- and high-Q2 values the extractions of the two-photon-exchange (TPE) amplitudes and the ratio Pl/PlBorn(Ïµ,Q2) using world data on electron-proton elastic scattering cross section

$σ$ R(Ïµ,Q2) with an emphasis on data covering the high-momentum region, up to Q2=5.20(GeV/c)2, to better constrain the TPE amplitudes in this region. We provide a new parametrization of the TPE amplitudes, along with an estimate of the fit uncertainties. We compare the results to several previous phenomenological extractions and hadronic TPE predictions. We use the new parametrization of the TPE amplitudes to extract the ratio Pl/PlBorn(Ïµ,Q2), and then compare the results to previous extractions, several theoretical calculations, and direct measurements at Q2=2.50(GeV/c)2.

2017 (2)

A robust inversion method for quantitative 3D shape reconstruction from coaxial eddy-current measurements. Haddar, H.; Riahi, M. M. K.; Jiang, Z.; and Riahi, M. M. K. Journal of Scientific Computing, 70(1): 29–59 (30). feb 2017.

A robust inversion method for quantitative 3D shape reconstruction from coaxial eddy-current measurements [pdf]

Paper doi link bibtex abstract

@article{2015arXiv150206723H,
abstract = {This work is motivated by the monitoring of conductive clogging deposits in steam generator at the level of support plates. One would like to use monoaxial coils measurements to obtain estimates on the clogging volume. We propose a 3D shape optimization technique based on simplified parametrization of the geometry adapted to the measurement nature and resolution. The direct problem is modeled by the eddy current approximation of time-harmonic Maxwell's equations in the low frequency regime. A potential formulation is adopted in order to easily handle the complex topology of the industrial problem setting. We first characterize the shape derivatives of the deposit impedance signal using an adjoint field technique. For the inversion procedure, the direct and adjoint problems have to be solved for each coil vertical position which is excessively time and memory consuming. To overcome this difficulty, we propose and discuss a steepest descent method based on a fixed and invariant triangulation. Numerical experiments are presented to illustrate the convergence and the efficiency of the method.},
archivePrefix = {arXiv},
arxivId = {math.NA/1502.06723},
author = {Haddar, Houssem and Riahi, M.{\~{}}K. Mohamed Kamel and Jiang, Zixian and Riahi, M.{\~{}}K. Mohamed Kamel},
doi = {http://arxiv.org/pdf/1502.06723.pdf},
eprint = {1502.06723},
isbn = {1091501602},
issn = {08857474},
journal = {Journal of Scientific Computing},
keywords = {Electromagnetism,Inverse problem,Mathematics - Analysis of PDEs,Mathematics - Numerical Analysis,Mathematics - Optimization and Control,Non-destructive testing,Shape optimization,Time-harmonic eddy current},
month = {feb},
number = {1},
pages = {29--59 (30)},
primaryClass = {math.NA},
title = {{A robust inversion method for quantitative 3D shape reconstruction from coaxial eddy-current measurements}},
url = {http://arxiv.org/pdf/1502.06723.pdf},
volume = {70},
year = {2017}
}

Well-conditioned boundary integral equation formulations and nystrm discretizations for the solution of Helmholtz problems with impedance boundary conditions in two-dimensional Lipschitz domains. Turc, C.; Boubendir, Y.; and Riahi, M. K. Journal of Integral Equations and Applications, 29(3). 2017.
doi link bibtex abstract

@article{Turc2017,
abstract = {{\textcopyright} 2017 Rocky Mountain Mathematics Consortium. We present a regularization strategy that leads to well-conditioned boundary integral equation formulations of Helmholtz equations with impedance boundary conditions in two-dimensional Lipschitz domains. We consider both the case of classical impedance boundary conditions, as well as that of transmission impedance conditions wherein the impedances are certain coercive operators. The latter type of problem is instrumental in the speed-up of the convergence of Domain Decomposition Methods for Helmholtz problems. Our regularized formulations use as unknowns the Dirichlet traces of the solution on the boundary of the domain. Taking advantage of the increased regularity of the unknowns in our formulations, we show through a variety of numerical results that a graded-mesh, based Nystr{\"{o}}m discretization of these regularized formulations leads to efficient and accurate solutions of interior and exterior Helmholtz problems with impedance boundary conditions.},
author = {Turc, C. and Boubendir, Y. and Riahi, M. K.},
doi = {10.1216/JIE-2017-29-3-441},
issn = {08973962},
journal = {Journal of Integral Equations and Applications},
keywords = {Graded meshes, Impedance boundary value problems, Integral equations, Lipschitz domains,Nystrm method, Regularizing operators},
number = {3},
title = {{Well-conditioned boundary integral equation formulations and nystrm discretizations for the solution of Helmholtz problems with impedance boundary conditions in two-dimensional Lipschitz domains}},
volume = {29},
year = {2017}
}

2016 (5)

Improved non-overlapping domain decomposition algorithms for the eddy current problem. Boubendir, Y; Haddar, H; and Riahi, M. jan 2016.

Improved non-overlapping domain decomposition algorithms for the eddy current problem [pdf]

Paper link bibtex abstract

@unpublished{Boubendir2016,
abstract = {A domain decomposition method is proposed based on carefully chosen impedance transmission operators for a hybrid formulation of the eddy current problem. Preliminary analysis and numerical results are provided in the spherical case showing the potential of these conditions in accelerating the convergence rate.},
archivePrefix = {arXiv},
arxivId = {math.NA/1602.00294},
author = {Boubendir, Y and Haddar, H and Riahi, M.{\~{}}K.},
booktitle = {ArXiv e-prints},
eprint = {1602.00294},
keywords = {Mathematics - Analysis of PDEs,Mathematics - Numerical Analysis},
month = {jan},
primaryClass = {math.NA},
title = {{Improved non-overlapping domain decomposition algorithms for the eddy current problem}},
url = {http://arxiv.org/pdf/1602.00294v1.pdf},
year = {2016}
}

On the use of the CFS-PML as a Laplace preconditioner in the FEM solution of elliptic scattering problems. Boubendir, Y; P., P.; and Riahi, M. ArXiv e-prints. 2016.

On the use of the CFS-PML as a Laplace preconditioner in the FEM solution of elliptic scattering problems [pdf]

Paper link bibtex

@article{BRTCornersImpedance,
archivePrefix = {arXiv},
arxivId = {math.NA/--},
author = {Boubendir, Y and P., Petropoulos and Riahi, M.{\~{}}K..},
eprint = {--},
journal = {ArXiv e-prints},
keywords = {CFS-Preconditioner,Mathematics - Numerical Analysis,PML - Mathematics - Analysis of PDEs,acoustics wave},
primaryClass = {math.NA},
title = {{On the use of the CFS-PML as a Laplace preconditioner in the FEM solution of elliptic scattering problems}},
url = {http://arxiv.org/pdf/1602.00294v1.pdf},
year = {2016}
}

NySL++: Nyström Scattering Library for the numerical approximation of the solution of Helmholtz equation in 2-dimension space for domain with corners. Kamel, R. M.; and Catalin, C. Newark, New Jersey USA, 2016.

Paper doi link bibtex

@manual{Nysl++,
address = {Newark, New Jersey USA},
author = {Kamel, Riahi Mohamed and Catalin, C-turc},
doi = {https://github.com/riahimk/RCFIE},
keywords = {Integral equations - Mathematics - Analysis of PDE},
title = {{NySL++: Nystr{\"{o}}m Scattering Library for the numerical approximation of the solution of Helmholtz equation in 2-dimension space for domain with corners}},
url = {data/preprint/nyslppCoversheet.pdf},
year = {2016}
}

A fast eddy-current non destructive testing finite element solver in steam generator. Riahi, M. K. Journal of Coupled Systems and Multiscale Dynamics, 4(1): 60–68. feb 2016.

A fast eddy-current non destructive testing finite element solver in steam generator [link]

Paper doi link bibtex abstract

@article{Riahi2016,
abstract = {In this paper we present an advanced numerical method to simulate a challenging industrial problem that consists in the non-destructive testing in steam generators. We develop a finite element technique that handles the big data systems arising from a discretization of the eddy-current equation in three dimensions. With high performance techniques, our method becomes fully efficient; the computational time is approximately divided by the number of available processors. We provide the results of numerical simulations using the software Freefem++, which has a powerful tool to handle finite element method and parallel computing. We show that our technique speeds up the simulation and exhibits full efficiency with respect to the number of processors used.},
archivePrefix = {arXiv},
arxivId = {math.NA/1602.03207},
author = {Riahi, M. K.},
doi = {10.1166/jcsmd.2016.1096},
eprint = {1602.03207},
issn = {2330152X},
journal = {Journal of Coupled Systems and Multiscale Dynamics},
month = {feb},
number = {1},
pages = {60--68},
primaryClass = {math.NA},
title = {{A fast eddy-current non destructive testing finite element solver in steam generator}},
url = {http://arxiv.org/pdf/1602.03207.pdf http://openurl.ingenta.com/content/xref?genre=article{\&}issn=2330-152X{\&}volume=4{\&}issue=1{\&}spage=60},
volume = {4},
year = {2016}
}

Fully efficient time-parallelized quantum optimal control algorithm. Riahi, M. K.; Salomon, J.; Glaser, S. J.; and Sugny, D. Physical Review A, 93(4). 2016.
doi link bibtex abstract 1 download

@article{Riahi2016a,
abstract = {We present a time-parallelization method that enables one to accelerate the computation of quantum optimal control algorithms. We show that this approach is approximately fully efficient when based on a gradient method as optimization solver: the computational time is approximately divided by the number of available processors. The control of spin systems, molecular orientation, and Bose-Einstein condensates are used as illustrative examples to highlight the wide range of applications of this numerical scheme.},
author = {Riahi, M. K. and Salomon, J. and Glaser, S. J. and Sugny, D.},
doi = {10.1103/PhysRevA.93.043410},
issn = {24699934},
journal = {Physical Review A},
number = {4},
title = {{Fully efficient time-parallelized quantum optimal control algorithm}},
volume = {93},
year = {2016}
}

2015 (1)

A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition. Riahi, M. K. Numerical Algorithms,1–32. 2015.

A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition [link]

Paper doi link bibtex abstract

@article{Riahi2015,
abstract = {In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization, our method involves Newton technique to compute the step-lengths for the sub-blocs resulting descent directions. Our optimization method is fully parallel and easily implementable, we first presents it in a general linear algebra setting, then we highlight its applicability to a parabolic optimal control problem, where we consider the blocs of unknowns with respect to the time dependency of the control variable. The parallel tasks, in the last problem, turn ``on'' the control during a specific time-window and turn it ``off'' elsewhere. We show that our algorithm significantly improves the computational time compared with recognized methods. Convergence analysis of the new optimal control algorithm is provided for an arbitrary choice of partition. Numerical experiments are presented to illustrate the efficiency and the rapid convergence of the method.},
author = {Riahi, M. K.},
doi = {10.1007/s11075-015-0060-0},
issn = {1572-9265},
journal = {Numerical Algorithms},
pages = {1--32},
title = {{A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition}},
url = {http://dx.doi.org/10.1007/s11075-015-0060-0},
year = {2015}
}

2014 (4)

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model. Baudron, A.; Lautard, J.; Maday, Y.; Riahi, M.; and Salomon, J. Journal of Computational Physics, 279: 67–79. 2014.
doi link bibtex abstract

@article{Baudron2014,
abstract = {{\textcopyright} 2014 Elsevier Inc.In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a $\theta$-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch-Maurer-Werner benchmark.},
author = {Baudron, A.-M. and Lautard, J.-J. and Maday, Y. and Riahi, M.K. and Salomon, J.},
doi = {10.1016/j.jcp.2014.08.037},
issn = {10902716},
journal = {Journal of Computational Physics},
keywords = {High performance computing,Parareal in time algorithm,Time-dependent neutron diffusion equations},
pages = {67--79},
title = {{Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model}},
volume = {279},
year = {2014}
}

© 2014 Elsevier Inc.In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a

$θ$ -scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch-Maurer-Werner benchmark.

Parareal in time 3D numerical solver for the \LWR\ Benchmark neutron diffusion transient model. Baudron, A.; Lautard, J.; Maday, Y.; Riahi, M. K.; and Salomon, J. Journal of Computational Physics, 279: 67–79. 2014.
$Parareal in time 3D numerical solver for the \LWR\ Benchmark neutron diffusion transient model [link]$ Paper doi link bibtex abstract

@article{Baudron201467,
abstract = {Abstract In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a $\theta$-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the LangenbuchâMaurerâWerner benchmark. },
author = {Baudron, Anne-Marie and Lautard, Jean-Jacques and Maday, Yvon and Riahi, Mohamed Kamel and Salomon, Julien},
doi = {http://dx.doi.org/10.1016/j.jcp.2014.08.037},
issn = {0021-9991},
journal = {Journal of Computational Physics},
keywords = {High performance computing,Parareal in time algorithm,Time-dependent neutron diffusion equations},
pages = {67--79},
title = {{Parareal in time 3D numerical solver for the {\{}LWR{\}} Benchmark neutron diffusion transient model}},
url = {http://www.sciencedirect.com/science/article/pii/S0021999114006056},
volume = {279},
year = {2014}
}

Abstract In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a

3D direct and inverse solvers for eddy current testing of deposits in steam generator. Haddar, H; and Riahi, M. K. Inria Research Reprt. jul 2014.

3D direct and inverse solvers for eddy current testing of deposits in steam generator [link]

Paper link bibtex

@article{2014arXiv1407.6237H,
archivePrefix = {arXiv},
arxivId = {physics.comp-ph/1407.6237},
author = {Haddar, H and Riahi, M. K.},
eprint = {1407.6237},
journal = {Inria Research Reprt},
keywords = {Physics - Computational Physics},
month = {jul},
primaryClass = {physics.comp-ph},
title = {{3D direct and inverse solvers for eddy current testing of deposits in steam generator}},
url = {http://arxiv.org/abs/1502.06723},
year = {2014}
}

3D direct and inverse solvers for eddy current testing of deposits in steam generator. Haddar, H; and Riahi, M. Inria Research Reprt. jul 2014.

Paper link bibtex

@article{Haddar2014,
archivePrefix = {arXiv},
arxivId = {physics.comp-ph/1407.6237},
author = {Haddar, H and Riahi, M.{\~{}}K.},
eprint = {1407.6237},
journal = {Inria Research Reprt},
keywords = {Physics - Computational Physics},
month = {jul},
primaryClass = {physics.comp-ph},
title = {{3D direct and inverse solvers for eddy current testing of deposits in steam generator}},
url = {http://arxiv.org/abs/1502.06723},
year = {2014}
}

2013 (1)

Control an. Maday, Y.; Riahi, M.; and Salomon, J. Control and Optimization with PDE Constraints, pages 79–92. Bredies, K.; Clason, C.; Kunisch, K.; and Winckel, G., editor(s). Springer Basel, Basel, Springer B edition, 2013.

Control and Optimization with PDE Constraints [link]

Paper doi link bibtex abstract

@inbook{Maday2013,
abstract = {In this paper, we present a method that enables to solve in parallel the EulerâLagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets that gives rise to independent sub-problems that can be solved in parallel. This method can be coupled with the parareal in time algorithm. Numerical experiments show the efficiency of our method.},
address = {Basel},
author = {Maday, Yvon and Riahi, Mohamed-Kamel and Salomon, Julien},
booktitle = {International Series of Numerical Mathematics},
chapter = {Control an},
doi = {10.1007/978-3-0348-0631-2_5},
edition = {Springer B},
editor = {Bredies, Kristian and Clason, Christian and Kunisch, Karl and Winckel, Gregory},
isbn = {978-3-0348-0631-2},
keywords = {Control Optimization PDEs Parareal in time algorit},
pages = {79--92},
publisher = {Springer Basel},
title = {{Control and Optimization with PDE Constraints}},
url = {http://dx.doi.org/10.1007/978-3-0348-0631-2{\_}5},
year = {2013}
}

2012 (1)

Conception et analyse d'algorithmes parallles en temps pour l'acceleration de simulations numriques d'\equations d'evolution. Riahi, M. K. Ph.D. Thesis, Universite Pierre et Marie Curie, Paris 6, Jussieu, 2012.
$Conception et analyse d'algorithmes parallles en temps pour l'acceleration de simulations numriques d'\equations d'evolution [link]$ Paper link bibtex abstract

@phdthesis{riahi2012conception,
abstract = {This thesis presents algorithms allowing parallelization in the time direction in the simulation of systems, which are governed by partial differential equations. These methods are applied in three application fields, and complex models. $\backslash$textbf{\{}1. Parabolic Optimal Control:{\}}$\backslash$$\backslash$ We develop two parallel algorithms (SITPOC and PITPOC). These two algorithms are based on a general method of time domain decomposition of optimal control problems. A convergence result for SITPOC is obtained. Moreover, a matrix interpretation for both algorithms is also given. $\backslash$textbf{\{}2. Kinetics of the population of neutrons in a nuclear reactor:{\}}$\backslash$$\backslash$ We design a parallel in time solver gathering all the variables associated with a nuclear reactor. Our method is adapted to various possible scenarios used in model reduction. The results of this solver are comparable with those obtained by the MINOS code of the CEA. The time parallelization is based on a parareal in time scheme for the time resolution. We consider several physical models of the kinetics of the neutrons. We simulate these models with the parareal in time algorithm in which the coarse solver corresponds to a reduced physical model. This reduction allows an important acceleration of the computational time. $\backslash$textbf{\{}3. Pulse sequence design in nuclear magnetic resonance and quantum information:{\}}$\backslash$$\backslash$ This chapter presents preliminary work on a time-parallel method for the resolution of an optimal control problem related to magnetic nuclear resonance. Our method produces an important acceleration compared with the nonparallel version. Moreover, the control fields computed with our method are smooth, which allows a simpler experimental implementation. Numerical tests prove the efficiency of our approach. On academic examples and without optimizing the code, we obtain significant improvements.},
author = {Riahi, Mohamed Kamel},
school = {Universite Pierre et Marie Curie, Paris 6, Jussieu},
title = {{Conception et analyse d'algorithmes parallles en temps pour l'acceleration de simulations numriques d'{\{}equations d'evolution}},
type = {Universite Paris-Sorbonne - Paris IV, 2012. Fran{\c{c}}ais},
url = {https://tel.archives-ouvertes.fr/tel-00870821/},
year = {2012}
}

This thesis presents algorithms allowing parallelization in the time direction in the simulation of systems, which are governed by partial differential equations. These methods are applied in three application fields, and complex models.

$\$textbf\1. Parabolic Optimal Control:\$\$$ \

$We develop two parallel algorithms (SITPOC and PITPOC). These two algorithms are based on a general method of time domain decomposition of optimal control problems. A convergence result for SITPOC is obtained. Moreover, a matrix interpretation for both algorithms is also given.$ \

$textbf\2. Kinetics of the population of neutrons in a nuclear reactor:\$\$$ \

$We design a parallel in time solver gathering all the variables associated with a nuclear reactor. Our method is adapted to various possible scenarios used in model reduction. The results of this solver are comparable with those obtained by the MINOS code of the CEA. The time parallelization is based on a parareal in time scheme for the time resolution. We consider several physical models of the kinetics of the neutrons. We simulate these models with the parareal in time algorithm in which the coarse solver corresponds to a reduced physical model. This reduction allows an important acceleration of the computational time.$ \

$textbf\3. Pulse sequence design in nuclear magnetic resonance and quantum information:\$\$$ \$ This chapter presents preliminary work on a time-parallel method for the resolution of an optimal control problem related to magnetic nuclear resonance. Our method produces an important acceleration compared with the nonparallel version. Moreover, the control fields computed with our method are smooth, which allows a simpler experimental implementation. Numerical tests prove the efficiency of our approach. On academic examples and without optimizing the code, we obtain significant improvements.

2011 (1)

An intermediate target method for the control of parabolic systems. Maday, Y.; Riahi, M.; and Salomon, J. In TAMTAM'11, Proceedings of the 5th conference on Trends in Applied Mathematics in Tunisia, Algeria, Morocco, 2011.

An intermediate target method for the control of parabolic systems [pdf]

Paper link bibtex abstract

@inproceedings{Maday2011,
abstract = {In this paper, we present a method that enables to solve in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of inter- mediate targets and gives rise independent sub-problems that can be solved in parallel. Numerical experiments show the efficiency of our method},
author = {Maday, Yvon and Riahi, Mohamed-Kamel and Salomon, Julien},
booktitle = {TAMTAM'11, Proceedings of the 5th conference on Trends in Applied Mathematics in Tunisia, Algeria, Morocco},
isbn = {978-9973-37-662-6},
title = {{An intermediate target method for the control of parabolic systems}},
url = {http://arxiv.org/pdf/1110.4084.pdf},
year = {2011}
}

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Mohamed Kamel RIAHI, Ph.D. Paris 6.

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