Contributions to Books:
M. Aurada, M. Ebner, M. Feischl, S. Ferraz-Leite, T. Führer, P. Goldenits, M. Karkulik, D. Praetorius:
"HILBERT, a MATLAB implementation of adaptive BEM (Release 3)";
in: "ASC Report 26/2013",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
The Matlab BEM library HILBERT allows the numerical solution of the 2D Laplace equation on some bounded Lipschitz domain with mixed boundary conditions by use of an adaptive Galerkin boundary element method (BEM). This paper provides a documentation of
HILBERT. The reader will be introduced to the data structures of HILBERT and mesh-refinement strategies. We discuss our approach of solving the Dirichlet problem (Section 5), the Neumann
problem (Section 6), the mixed boundary value problem with Dirichlet and Neumann boundary conditions (Section 7), and the extension to problems with non-homogeneous volume forces (Section 8). Besides a brief introduction to these problems, their equivalent integral
formulations, and the corresponding BEM discretizations, we put an emphasis on possible strategies to steer an adaptive mesh-refining algorithm. In particular, various error estimators are discussed.
Another notable feature is a complete and detailed description of our Matlab implementation which enhances the readerīs understanding of how to use the HILBERT program package.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.