Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations

Abstract : In this paper, we extend the reduced-basis approximations developed earlier for linear elliptic and parabolic partial differential equations with affine parameter dependence to problems involving (a) nonaffine dependence on the parameter, and (b) nonlinear dependence on the field variable. The method replaces the nonaffine and nonlinear terms with a coefficient function approximation which then permits an efficient offline-online computational decomposition. We first review the coefficient function approximation procedure: the essential ingredients are (i) a good collateral reduced-basis approximation space, and (ii) a stable and inexpensive interpolation procedure. We then apply this approach to linear nonaffine and nonlinear elliptic and parabolic equations; in each instance, we discuss the reduced-basis approximation and the associated offline-online computational procedures. Numerical results are presented to assess our approach.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00112154
Contributor : Pascal Joly <>
Submitted on : Friday, November 10, 2006 - 10:38:36 AM
Last modification on : Sunday, March 31, 2019 - 1:34:43 AM
Long-term archiving on : Tuesday, April 6, 2010 - 9:46:44 PM

Identifiers

  • HAL Id : hal-00112154, version 1

Citation

Martin A. Grepl, Yvon Maday, N.C. Nguyen, Anthony T. Patera. Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. 2006. ⟨hal-00112154⟩

Share

Metrics

Record views

447

Files downloads

506