A wirebasket preconditioner for the mortar boundary element method
Thomas Führer and Norbert Heuer
Adv. Comput. Math. 44 (1), 23-49, 2018.
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.