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Model reduction using L 1 ‐norm minimization as an application to nonlinear hyperbolic problems
Author(s) -
Abgrall R.,
Crisovan R.
Publication year - 2018
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4507
Subject(s) - continuation , minification , nonlinear system , mathematics , reduction (mathematics) , scalar (mathematics) , norm (philosophy) , compressibility , mathematical optimization , computer science , geometry , physics , quantum mechanics , political science , law , thermodynamics , programming language
Summary We are interested in the model reduction techniques for hyperbolic problems, particularly in fluids. This paper, which is a continuation of an earlier paper of Abgrall et al, proposes a dictionary approach coupled with an L 1 minimization approach. We develop the method and analyze it in simplified 1‐dimensional cases. We show in this case that error bounds with the full model can be obtained provided that a suitable minimization approach is chosen. The capability of the algorithm is then shown on nonlinear scalar problems, 1‐dimensional unsteady fluid problems, and 2‐dimensional steady compressible problems. A short discussion on the cost of the method is also included in this paper.