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What is epsBEM?

epsBEM is a MATLAB software package for the solution of 2D Laplace- and Lamé equations using hp Boundary Element Methods. It allows for the computation with large polynomial degrees (p>1000) while still providing efficient and stable routines.
Using Legendre polynomials and Lobatto shape functions as ansatz functions results in simple recurrence relations and gives a relation to Legendre functions of the second kind. This enables us to calculate potentials and Galerkin entries even for high polynomial degrees in an efficient way close to machine precision. The stability of the functions is achieved by a combination of forward an backward recurrence relations for the potentials and the use of high precision libraries such as mpfr and mpc for the Galerkin entries, respectively.
The core of the software package is made up of a C-library that contains procedures for the evaluation of Legendre functions and their integrals. The top-layer of the software package, which consists of the user interface and other functions the user would be interested in, is programmed in MATLAB. This combination of C and MATLAB results in a software package that provides not only very efficient and stable procedures but is also easy to use. Therefore it is useful for both teaching and research.

Developers

Andreas Bantle
Markus Bantle
Stefan Funken