ECCOMAS 2024

Non-intrusive implementation of the Multiscale Finite Element Method

  • Legoll, Frederic (ENPC and Inria)

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The Multiscale Finite Element Method (MsFEM) is a well established numerical approach dedicated to multiscale problems. In its standard implementation, MsFEM first precomputes (in an offline stage) a problem dependent basis, consisting of local, highly oscillatory, non polynomial basis functions. It next performs (in a online stage) a Galerkin approximation of the problem on the discretization space built in the offline stage. As such, the method cannot be straightforwardly implemented in a generic Finite Element (FE) code, which hinders its adoption in non-academic environments. In this talk, we show how to slightly modify the method in order to allow for a non-intrusive implementation. It actually amounts to translating the method into an effective, single scale, problem, which can be solved by a generic FE software. Several numerical examples will be discussed, showing that the modified method shares the same accuracy as the original method. Joint work with Rutger Biezemans, Claude Le Bris (ENPC and Inria) and Alexei Lozinski (Univ. Franche-Comte).