Welcome to NGSBEM

Welcome to NGSBEM#

NGSBEM implements boundary integral operators on top of [NGSolve].

It currently supports single-layer, double-layer, and hypersingular operators for:

  • Laplace equation

  • Helmholtz equation

  • Maxwell equation

The software works with high-order function spaces on curved surface meshes.
Numerical integration follows [SS09], while matrix compression and potential evaluation are based on the Fast Multipole Method [RG85].

NGSBem achieves high-order convergence rates such as presented and discussed in [Weg11].

Install a NGSolve release and try notebooks from the GitHub demos folder.

Overview

The repository combines practical demos with a theoretical introduction to BEM:

Short and Sweet: Introduction to BEM and Software Capabilities

This section gives a concise overview of the Boundary Element Method (BEM) and the features of NGSBem.
It highlights the convergence rates achievable for different problems.

Demos: Step-by-Step from PDE to BEM Solution

The demos show how to solve concrete problems using NGSBEM:

  • Explain the connection between linear operators and the boundary value problem.

  • Show step by step how the problem is translated into the boundary element method.

  • Introduce software-specific operators and key implementation details.

These demos provide a hands-on view of the workflow, making the theory concrete.

Background: Theoretical Foundations

This section introduces energy spaces and trace spaces.

  • Unlike FEM, BEM operates on the boundary, not the full PDE domain.

  • Function spaces are therefore discretized on the boundary.

  • All relevant potentials forming the starting point of BEM are presented.

The presentation is theoretical and mainly follows [SS09] and [Weg11].

Overall, the repository offers a hands-on introduction to NGSBEM, linking practical demos to a concise summary of the theoretical foundations.
Explore it on GitHub: Weggler/docu-ngsbem.