We define and analyze (local) multilevel diagonal preconditioners for isogeometric boundary elements on locally refined meshes in two dimensions. Hypersingular and weakly-singular integral equations are considered. We prove that the condition number of the preconditioned systems of linear equations is independent of the mesh-size and the refinement level. Therefore, the computational complexity, when using appropriate iterative solvers, is optimal. Our analysis is carried out for closed and open boundaries and numerical examples confirm our theoretical results.
@article{arxiv.1808.04585,
title = {Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods},
author = {Thomas Führer and Gregor Gantner and Dirk Praetorius and Stefan Schimanko},
journal= {arXiv preprint arXiv:1808.04585},
year = {2019}
}
Comments
accepted in Computer Methods in Applied Mechanics and Engineering