Welcome to NG-BEM

NG-BEM 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

NG-BEM supports high order function spaces on curved surface meshes. It uses numerical integration following [Sauter-Schwab: Boundary Element Methods, 2009], and matrix compression based on the ACA algorithm [Bebendorf: Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems, 2008]

Installation:

• Install a recent NGSolve (later than Feb. 10, 2024)

• Install ngbem from github:

  git clone https://github.com/Weggler/ngbem.git
  cd ngbem
  mkdir build
  cd build
  cmake ..
  make -j4 install
  

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

Short and Sweet

• Boundary Element Method
• BIE for Laplace
• Laplace Demo 1
• Laplace Demo 2
• Laplace Demo 3
• BIE for Maxwell
• Maxwell Demo 1
• Maxwell Demo 2
• Convergence Rates

Detailed Demos

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