An Algebraic Local Generalized Eigenvalue in the Overlapping Zone Based Coarse Space : A first introduction

Nicole Spillane (1, 2) , Victorita Dolean (3) , Patrice Hauret (4) , Frédéric Nataf (1, 2) , Clemens Pechstein (5) , Robert Scheichl (6)

1 LJLL - Laboratoire Jacques-Louis Lions
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
3 JAD - Laboratoire Jean Alexandre Dieudonné
4 Centre de Technologie de Ladoux
5 Institute of Computational Mathematics
6 Department of Mathematical Sciences [Bath]

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods. However, it is known that most popular choices of coarse spaces perform rather weakly in presence of heterogeneities in the coefficients in the partial differential equations, especially for systems. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems which isolate the terms responsible for slow convergence. We give a general theoretical result and then some numerical examples on a heterogeneous elasticity problem.

Domaines: Analyse numérique [math.NA]

Nicole Spillane, Victorita Dolean, Patrice Hauret, Frédéric Nataf, Clemens Pechstein, et al.. An Algebraic Local Generalized Eigenvalue in the Overlapping Zone Based Coarse Space : A first introduction. 2011. ⟨hal-00630892⟩