Welcome to NGSBEM

NGSBem implements boundary integral operators on top of NGSolve.

Currently it supports single-layer and double-layer operators and hypersingular operators for the

• Laplace equation

• Helmholtz equation

• Maxwell equation

NGSBem supports high order function spaces on curved surface meshes. It uses numerical integration following [Sauter-Schwab: Boundary Element Methods, 2009], and matrix compression and potential evalution based on the Fast Multipole Method [Rokhlin, Greengard, Rapid Solution of Integral Equations of Classic Potential Theory, 1985].

Installation:

• Install a recent NGSolve (later than August 25, 2025)

Try notebooks from the demos folder. You can read (only read) them directly on github: Weggler/docu-ngsbem

Short and Sweet

• Boundary Element Method
• BIE for Laplace
• BIE for Maxwell
• Convergence Rates

Detailed Demos

• Dirichlet Laplace Indirect Method
• Dirichlet Laplace Direct Method
• Neumann Laplace Indirect Method
• Neumann Laplace Direct Method
• Laplace with Mixed Conditions
• BEM Laplace Capacitor
• Laplace FEM-BEM Coupling
• Maxwell PEC Indirect Method
• Maxwell PEC Direct method
• Maxwell Mixed Conditions