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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.

@article{riahiNCG18, 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.}, address = {Newark, New Jersey USA}, annote = {From Duplicate 10 (TOWARDS A FULLY SCALABLE BALANCED PARAREAL METHOD: APPLICATION TO NEUTRONICS - Maday, Yvon; Mula, Olga; Riahi, Mohamed-Kamel) working paper or preprint}, archivePrefix = {arXiv}, arxivId = {math.NA/1602.03207}, author = {Astanina, Marina S. and {Kamel Riahi}, Mohamed and Abu-Nada, Eiyad and Sheremet, Mikhail A. and Baudron, A.-M. and Lautard, J.-J. and Maday, Yvon and Riahi, M.{\~{}}K. Mohamed-Kamel M.{\~{}}K.. K Mohamed Kamel M.K. K. and Salomon, Julien and Boubendir, Y and Haddar, H and Riahi, M.{\~{}}K. Mohamed-Kamel M.{\~{}}K.. K Mohamed Kamel M.K. K. and P., Petropoulos and Riahi, M.{\~{}}K. Mohamed-Kamel M.{\~{}}K.. K Mohamed Kamel M.K. K. and Haddar, H and Riahi, M.{\~{}}K. Mohamed-Kamel M.{\~{}}K.. K Mohamed Kamel M.K. K. and Kamel, Riahi Mohamed and Catalin, C-turc and {M. K. Riahi I. A. Qattan}, J Hassan and Homouz, D. and Maday, Yvon and Mula, Olga and Riahi, M.{\~{}}K. Mohamed-Kamel M.{\~{}}K.. K Mohamed Kamel M.K. K. and Salomon, Julien and Qattan, I. A. and Homouz, D. and Riahi, M.{\~{}}K. Mohamed-Kamel M.{\~{}}K.. K Mohamed Kamel M.K. K. and Qattan, I. A. and Salomon, Julien and Glaser, S J and Sugny, D}, doi = {10.1166/jcsmd.2016.1096}, eprint = {1602.03207}, institution = {Universit{\{}{\'{e}}{\}} Pierre et Marie Curie, Paris 6, Jussieu}, isbn = {978-9973-37-662-6}, issn = {24699993}, journal = {International Journal of Heat and Mass Transfer}, keywords = {CFS-Preconditioner,Convergence analysis,Dynamical systems,Eddy-Current approximation,Finite element,Heat transfer enhancement,High performance computing,Industrial problem.,Integral equations - Mathematics - Analysis of PDE,Magnetohydrodynamics,Mathematics - Analysis of PDEs,Mathematics - Numerical Analysis,Maxwell's Equations,Nanofluid,Natural convection,Non-destructive testing,Nonlinear Conjugate gradient methods,Nonlinear Optimal control,Numerical Methods,PML - Mathematics - Analysis of PDEs,Parallel Algorithm,Parameter estimation and Inverse problem,Parareal in time algorithm,Physics - Computational Physics,Time-dependent neutron diffusion equations,Variable properties,acoustics wave,degraded fine solver,parareal in time algorithm}, month = {feb}, number = {1}, pages = {532--548}, primaryClass = {math.NA}, publisher = {American Physical Society}, title = {{Magnetohydrodynamic in partially heated square cavity with variable properties: Discrepancy in experimental and theoretical conductivity correlations}}, type = {Universit{\'{e}} Paris-Sorbonne - Paris IV, 2012. Fran{\c{c}}ais}, url = {https://tel.archives-ouvertes.fr/tel-00870821/ https://doi.org/10.1166/jcsmd.2016.1096 http://arxiv.org/pdf/1602.03207.pdf http://openurl.ingenta.com/content/xref?genre=article{\&}issn=2330-152X{\&}volume=4{\&}issue=1{\&}spage=60 http://link.aps.org/doi/10.1103/PhysR}, volume = {4}, year = {2018} }

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