BEM3D: a free adaptive fast multipole boundary element library

TL;DR

BEM3D is a free, open-source boundary element library that employs a fast multipole method tailored for higher-order elements, enabling efficient and accurate solutions for complex geometries.

Contribution

It introduces a novel implementation of a fast multipole method specifically designed for higher-order boundary elements within an open-source library.

Findings

Accurate and convergent results on sphere and cube geometries

Efficient handling of sharp edges in boundary element calculations

Open-source library accessible under GPL license

Abstract

The design, implementation and analysis of a free library for boundary element calculations is presented. The library is free in the sense of the GNU General Public Licence and is intended to allow users to solve a wide range of problems using the boundary element method. The library incorporates a fast multipole method which is tailored to boundary elements of order higher than zero, taking account of the finite extent of the elements in the generation of the domain tree. The method is tested on a sphere and on a cube, to test its ability to handle sharp edges, and is found to be accurate, efficient and convergent.