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T. Führer, D. Praetorius, S. Schimanko:
"Adaptive BEM with inexact PCG solver yields almost optimal computational costs";
Hauptvortrag: Universität Bayreuth, Bayreuth (eingeladen); 11.12.2019.

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).

https://publik.tuwien.ac.at/files/publik_284137.pdf