Is a Lovely Boundary Element Research Tool


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

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.


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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

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

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