Publications in Scientific Journals:
T. Führer, G. Gantner, D. Praetorius, S. Schimanko:
"Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods";
Computer Methods in Applied Mechanics and Engineering,
351
(2019),
571
- 598.
English abstract:
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.
Keywords:
preconditioner, multilevel additive Schwarz, isogeometric analysis, boundary element methods.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.cma.2019.03.038
Created from the Publication Database of the Vienna University of Technology.