A nonintrusive method to approximate linear systems with nonlinear parameter dependence

Abstract : We consider a family of linear systems $A_\mu \alpha=C$ with system matrix $A_\mu$ depending on a parameter $\mu$ and for simplicity parameter-independent right-hand side $C$. These linear systems typically result from the finite-dimensional approximation of a parameter-dependent boundary-value problem. We derive a procedure based on the Empirical Interpolation Method to obtain a separated representation of the system matrix in the form $A_\mu\approx\sum_{m}\beta_m(\mu)A_{\mu_m}$ for some selected values of the parameter. Such a separated representation is in particular useful in the Reduced Basis Method. The procedure is called nonintrusive since it only requires to access the matrices $A_{\mu_m}$. As such, it offers a crucial advantage over existing approaches that instead derive separated representations requiring to enter the code at the level of assembly. Numerical examples illustrate the performance of our new procedure on a simple one-dimensional boundary-value problem and on three-dimensional acoustic scattering problems solved by a boundary element method.
Type de document :
Pré-publication, Document de travail
17 pages, 9 figures. 2013
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https://hal.archives-ouvertes.fr/hal-00845822
Contributeur : Fabien Casenave <>
Soumis le : mercredi 17 juillet 2013 - 21:08:56
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

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  • HAL Id : hal-00845822, version 1
  • ARXIV : 1307.4330

Citation

Fabien Casenave, Alexandre Ern, Tony Lelièvre, Guillaume Sylvand. A nonintrusive method to approximate linear systems with nonlinear parameter dependence. 17 pages, 9 figures. 2013. <hal-00845822>

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