Virtual charts of solutions for parametrized nonlinear equations

DOI10.1007/s00466-014-1073-6zbMath1309.74073OpenAlexW2072937002MaRDI QIDQ487887

Pierre-Alain Boucard, David Néron, Matthieu Vitse

Publication date: 23 January 2015

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00466-014-1073-6

zbMATH Keywords

nonlinear problemsreduced order modelingproper generalized decompositionLATIN solverparametric problems

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Uses Software

• rbMIT

Cites Work

• Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models
• Multiparametric analysis within the proper generalized decomposition framework
• A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations
• A priori hyperreduction method: an adaptive approach
• Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
• Reduced basis method for quadratically nonlinear transport equations
• Reduced-order fluid/structure modeling of a complete aircraft configuration
• On the stability of the reduced basis method for Stokes equations in parametrized domains
• An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
• A model reduction technique based on the PGD for elastic-viscoplastic computational analysis
• A rational strategy for the resolution of parametrized problems in the PGD framework
• A PGD-based homogenization technique for the resolution of nonlinear multiscale problems
• On the a priori model reduction: overview and recent developments
• A Generalized Empirical Interpolation Method: Application of Reduced Basis Techniques to Data Assimilation
• Proper generalized decomposition of time-multiscale models
• Nonlinear Model Reduction via Discrete Empirical Interpolation
• Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
• A computational strategy for poroelastic problems with a time interface between coupled physics
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