Contributions to Books:
T. Führer, G. Gantner, D. Praetorius, S. Schimanko:
"Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods";
in: "ASC Report 20/2018",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
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.
preconditioner, multilevel additive Schwarz, isogeometric analysis, boundary element methods.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.