Boundary Element Method#
What is a standard BEM problem?
One of the following pdes with given boundary condition:
Laplace equation
Helmholtz equation
Maxwells equations
Lamé equations
Stokes equations
How to derive a BEM from a standard BEM problem?
choose an ansatz for the solution of the pde in terms of layer potentials
derive a boundary integral equation for unknown density
discretize the resulting variational formulation with finite element spaces on the boundary
solve the system of linear equations and get the best approximation of the unknown density
evaluate the solution with the ansatz from 1. wherever you want inside the pde domain
Why is BEM beneficial?
problem dimension is reduced to the boundary of the pde domain, thus reduced by one
exterior problems are not an issue
the solution is very accurate
Why is BEM not everybodies darling?
only linear, isotropic material
source terms cause Newton potentials
singular integral kernels
dense matrices
NGSBem Keyfacts:
kernel-driven generic implementation of the layer potential operator
fast and accurate assembly of system matrices using MLFMM
fast and accurate assembly of potentials using MLFMM with nearfield considerations
compatible with NGSolve
user-friendly Python interface with declarative programming of variational formulations
potentials for all standard problems
tested and documented