Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equationsReport as inadecuate




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1 MIT-MECHE - Department of Mechanical Engineering 2 LJLL - Laboratoire Jacques-Louis Lions

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.





Author: Martin A. Grepl - Yvon Maday - N.C. Nguyen - Anthony T. Patera -

Source: https://hal.archives-ouvertes.fr/



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