Francisco Chinesta, Roland Keunings, Adrien Leygue's The Proper Generalized Decomposition for Advanced Numerical PDF

By Francisco Chinesta, Roland Keunings, Adrien Leygue

ISBN-10: 3319028650

ISBN-13: 9783319028651

Many difficulties in clinical computing are intractable with classical numerical innovations. those fail, for instance, within the answer of high-dimensional versions as a result exponential elevate of the variety of levels of freedom.

Recently, the authors of this ebook and their collaborators have constructed a unique process, referred to as right Generalized Decomposition (PGD) that has confirmed to be an important breakthrough. The PGD builds via a successive enrichment procedure a numerical approximation of the unknown fields in a separated shape. even though first brought and effectively confirmed within the context of high-dimensional difficulties, the PGD permits a very new procedure for addressing extra usual difficulties in technological know-how and engineering. certainly, many tough difficulties should be successfully solid right into a multi-dimensional framework, hence beginning completely new answer innovations within the PGD framework. for example, the cloth parameters and boundary stipulations showing in a specific mathematical version will be considered as extra-coordinates of the matter as well as the standard coordinates corresponding to area and time. within the PGD framework, this enriched version is solved just once to yield a parametric resolution that comes with all specific options for particular values of the parameters.

The PGD has now attracted the eye of a giant variety of learn teams world wide. the current textual content is the 1st to be had publication describing the PGD. It presents a truly readable and useful creation that enables the reader to fast snatch the most good points of the tactic. during the e-book, the PGD is utilized to difficulties of accelerating complexity, and the method is illustrated through rigorously chosen numerical examples. in addition, the reader has unfastened entry to the Matlab© software program used to generate those examples.

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Extra info for The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer (SpringerBriefs in Applied Sciences and Technology)

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Numerical Methods Biomed. Eng. 29(5), 586–600 (2013) 65. I. Alfaro, D. Gonzalez, F. Bordeu, A. Leygue, A. Ammar, E. Cueto, F. Chinesta, Real-time in sillico experiments on gene regulatory networks and surgery simulation on handheld devices, J. Comput. Surg. (in press) 66. A. Dumon, C. Allery, A. Ammar, Proper generalized decomposition method for incompressible Navier-Stokes equations with a spectral discretization. Appl. Math. Comput. 219(15), 8145– 8162 (2013) 67. A. Ammar, F. Chinesta, P. Diez, A.

Paris 309, 1095–1099 (1989) 20. P. -C. Passieux, D. Néron, The latin multiscale computational method and the proper generalized decomposition. Comput. Methods Appl. Mech. Eng. 199(21–22), 1287– 1296 (2010) 22 1 Introduction 21. D. Néron, P. Ladevèze, Proper generalized decomposition for multiscale and multiphysics problems. Arch. Comput. Methods Eng. 17(4), 351–372 (2010) 22. A. Nouy, P. Ladevèze, Multiscale computational strategy with time and space homogenization: a radial-type approximation technique for solving microproblems.

Among those, we could cite the optimality and robustness of separated representation constructors, a topic that requires further research in numerical analysis; domain partitioning (some preliminary but promising results exist by considering the Arlequin technique [81] within the PGD framework); solid mechanics with large material transformations (in that case, space and time cannot be directly separated); hyperbolic problems; non-linear multi parametric models; how to address discontinuities and localization; how to define bridges between the PDG and standard commercial simulation codes.

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The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer (SpringerBriefs in Applied Sciences and Technology) by Francisco Chinesta, Roland Keunings, Adrien Leygue


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