FWF Project P21732 Adaptive Boundary Element Method | Instiute for Analysis and Scientific Computing | TU Wien

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HILBERT
Is a Lovely Boundary Element Research Tool

Description

HILBERT is a Matlab library for h-adaptive Galerkin BEM. Currently, only lowest-order elements for the 2D Laplacian are implemented, i.e., piecewise constants P⁰ for fluxes and piecewise affine and globally continuous S¹ for traces of concentrations.

HILBERT is developed as the research code for the FWF project P21732 Adaptive Boundary Element Method. It will include the current state of the art and will provide the starting point for further investigations. HILBERT is free for academic use and might provide a good basis for academic education on BEM as well.

Further informations on HILBERT are available through

• the handout of a talk which announced the library (October 2009),
• the paper (open access) which recently appeared in Numer. Algorithms (September 2014),
• the exhaustive HILBERT documentation (June 2013).

Download HILBERT Library

HILBERT has been accepted for publication in Numer. Algorithms, and the software is available for download under http://www.netlib.org/numeralgo/. Further updates (FEM-BEM coupling, second-order elements, linear elasticity) will appear here for download.

Newsletter

You can subscribe the newsletter to keep up-to-date about improvements and extensions of HILBERT.

Features of HILBERT (Release 3, June 2012)

All Galerkin matrices are implemented in C through the Matlab MEX interface. They can thus be easily linked to any other programming language like Fortran, C, or C++. So far, HILBERT provides the following three discrete integral operators

• Newton potential N for P⁰ ansatz and test functions,
• simple-layer potential V for P⁰ ansatz and test functions,
• double-layer potential K for S¹ ansatz and P⁰ test functions,
• hypersingular integral operator W for S¹ ansatz and test functions.

Moreover, HILBERT provides functions, also implemented in C through the Matlab MEX interface, for the point evaluations of these operators as well as of the adjoint double-layer potential. The remaining Matlab codes are fully vectorized. By others, HILBERT includes

• different error estimators,
• h-h/2 error estimators (proposed by Ferraz-Leite, Praetorius & co-workers),
• two-level estimator (introduced by Maischak, Stephan & co-workers),
• weigthed-residual error estimators (introduced by Carstensen, Stephan & co-workers),
• different marking strategies,
• Dörfler' bulk criterion,
• maximum criterion,
• optimal local mesh-refinement for boundary meshes,
• newest vertex bisection to refine volume meshes,
• several visualization tools.

For the ease of introduction to adaptive BEM, HILBERT provides example files and adaptive algorithms for the integral formulations for

• the Dirichlet problem (so-called weakly-singular integral equation),
• the Neumann problem (so-called hypersingular integral equation),
• the mixed boundary value problem with Dirichlet/Neumann boundary conditions,
• with/without volume data,
• for different adaptive strategies from the literature,
• also for indirect BEM formulations.

Dirk Praetorius |  
TU Wien | Institute for Analysis and Scientific Computing | Wiedner Hauptstraße 8-10 | 1040 Wien, Austria
Fon: +43 1 58801-101 50 | Fax: +43 1 58801-101 96