A GenEO Domain Decomposition method for Saddle Point problems

Abstract

We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub matrices are sparse and that the diagonal blocks are spectrally equivalent to a sum of positive semi definite matrices. The latter assumption enables the design of adaptive coarse space for DD methods that extends the GenEO theory (Spillane et al., 2014) to saddle point problems. Numerical results on three dimensional elasticity problems for steel-rubber structures discretized by a finite element with continuous pressure are shown for up to one billion degrees of freedom.

Keywords

• domain decomposition method
• nearly incompressible elasticity
• high performance computing
• saddle point problem
• coarse space
• multiscale finite element
• Schur complement