Contributions to Books:
M. Aurada, M. Ebner, M. Feischl, S. Ferraz-Leite, T. Führer, P. Goldenits, M. Karkulik, M. Mayr, D. Praetorius:
"HILBERT - A MATLAB implementation of adaptive 2D-BEM";
in: "ASC Report 24/2011",
issued by: Institute of Analysis and Scientific Computing;
Vienna University of Technology,
We report on the Matlab program package HILBERT. It provides an easy-accessible implementation of lowest order adaptive Galerkin boundary element methods for the numerical solution of the Poisson equation in 2D. The library was designed to serve several purposes:
The stable implementation of the integral operators may be used in research code. The framework of Matlab ensures usability in lectures on boundary element methods or scientific computing. Finally, we aim at emphasizing the use of adaptivity as general concept and for boundary element methods in particular. In this work we summarize recent analytical results on adaptivity in the context of BEM and give sample code to illustrate the use of HILBERT. Various benchmarks are performed to empirically analyze the performance of the proposed adaptive algorithms and to compare adaptive and uniform mesh-refinement. In particular, we do not only focus on mathematical convergence behavior but also on the usage of critical system resources such as memory consumption and computational time. In any case, the superiority of the proposed adaptive approach is empirically supported.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.