Bembel: BEM-Based Engineering Library

Bembel is a Boundary Element Method Based Engineering Library written in C and C++ to solve boundary value problems governed by the Laplace, Helmholtz or electric wave equation [3,4,5]. It was written as part of a cooperation between the TU Darmstadt and the University of Basel, coordinated by H. Harbrecht, S. Kurz and S. Schöps. It is based on the Laplace BEM of J. Dölz, H. Harbrecht and M. Multerer, [2,6] as well as the spline and geometry framework of F. Wolf. We plan to release the code here under the GNU GPLv3 in early 2019.

Features

As of now, it supports arbitrary parametric mappings for the geometry representation, utilising an embedded interpolation-based fast multipole method for compression [2,4], equivalent to the H2 matrix format.
As ansatz functions, any type of piecewise polynomial functions of higher order can be constructed. Specifically, this includes conforming B-spline discretisations to operate within the framework of isogeometric analysis, cf. [1].

Planned features include a geometry import from geopdes and general octave wrappers.

Publications and Preprints

[1] A. Buffa, J. Dölz, S. Kurz, S. Schöps, R. Vázques and F. Wolf. Multipatch Approximation of the de Rham Sequence and its Traces in Isogeometric Analysis. Submitted. To the preprint.
[2] J. Dölz, H. Harbrecht and M. Peters: An interpolation-based fast multipole method for higher-order boundary elements on parametric surfaces. To the paper.
[3] J. Dölz, H. Harbrecht, S. Kurz, S. Schöps and F. Wolf. A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems. To the paper. To the preprint.
[4] J. Dölz, S. Kurz, S. Schöps and F. Wolf. Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples. Submitted. To the preprint.
[5] J. Dölz, S. Kurz, S. Schöps and F. Wolf. A Numerical Comparison of an Isogeometric and a Classical Higher-Order Approach to the Electric Field Integral Equation. Submitted. To the preprint.
[6] H. Harbrecht and M. Peters. Comparison of fast boundary element methods on parametric surfaces. To the paper.

Contributors

J. Dölz (Darmstadt), H. Harbrecht (Basel), M. Multerer (Lugano) and F. Wolf (Darmstadt).