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Preprints, Working Papers, ... Year : 2013

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.

Dates and versions

hal-00845822 , version 1 (17-07-2013)

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Fabien Casenave, Alexandre Ern, Tony Lelièvre, Guillaume Sylvand. A nonintrusive method to approximate linear systems with nonlinear parameter dependence. 2013. ⟨hal-00845822⟩
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