A wirebasket preconditioner for the mortar boundary element method

TL;DR

This paper introduces a new additive Schwarz preconditioner for the mortar boundary element method, improving solver efficiency through a stable wirebasket space decomposition applicable to various mesh types.

Contribution

It develops a novel wirebasket preconditioner with proven stability and efficiency for mortar boundary element methods, accommodating both uniform and non-uniform meshes.

Findings

Preconditioner achieves near-optimal condition numbers.

Numerical results confirm theoretical bounds.

Applicable to triangular and quadrilateral meshes.

Abstract

We present and analyze a preconditioner of the additive Schwarz type for the mortar boundary element method. As a basic splitting, on each subdomain we separate the degrees of freedom related to its boundary from the inner degrees of freedom. The corresponding wirebasket-type space decomposition is stable up to logarithmic terms. For the blocks that correspond to the inner degrees of freedom standard preconditioners for the hypersingular integral operator on open boundaries can be used. For the boundary and interface parts as well as the Lagrangian multiplier space, simple diagonal preconditioners are optimal. Our technique applies to quasi-uniform and non-uniform meshes of shape-regular elements. Numerical experiments on triangular and quadrilateral meshes confirm theoretical bounds for condition and MINRES iteration numbers.