Hinweis
Dieser Eintrag wurde automatisch aus einem Altsystem migriert. Die Daten wurden nicht überprüft und entsprechen eventuell nicht den Qualitätskriterien des vorliegenden Systems.
Führer, T., Praetorius, D., & Schimanko, S. (2019). Adaptive BEM with inexact PCG solver yields almost optimal computational costs. Universität Bayreuth, Bayreuth, Germany, Austria. http://hdl.handle.net/20.500.12708/122921
In our talk, we will sketch our recent work [Führer et al., Numerische Mathematik 141, 2019].
We consider the preconditioned conjugate gradient method (PCG) in the frame of the boundary
element method (BEM) with adaptive mesh-refinement. As model problem serves the
weakly-singular integral equation associated with the Laplace operator. We propose an adaptive
algorithm, which steers the loca...
In our talk, we will sketch our recent work [Führer et al., Numerische Mathematik 141, 2019].
We consider the preconditioned conjugate gradient method (PCG) in the frame of the boundary
element method (BEM) with adaptive mesh-refinement. As model problem serves the
weakly-singular integral equation associated with the Laplace operator. We propose an adaptive
algorithm, which steers the local mesh-refinement as well as the termination of PCG. We prove that
this algorithm leads to linear convergence with optimal algebraic rates. Moreover, if the preconditioner
is optimal (e.g., multi-level diagonal additive Schwarz preconditioner) and if we employ H2-matrices
for the effective treatment of the discrete integral operators, then the algorithm leads even to almost
optimal convergence rates with respect to the computational complexity (i.e., the computational time).
