# Boundary Element Method

Boundary Element Method (BEM) is a numerical method of solving partial differential equations (PDEs) presented in the integral form known as Boundary Integral Equation (BIE).

## Partial Differential Equations (PDEs)

The BEMLAB library has been implemented to support following PDEs:

- Laplace equation:

- Poisson equation:

- Helmholtz equation or Diffusion equation in frequency domain:

## Boundary Integral Equation (BIE)

Boundary Integral Equation (BIE) is the basic equation which is solved by BEM. PDEs have to be presented in the form of the following BIE:

where

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Omega}**- domain of the problem, where PDE is being solved,- - boundary of the investigated domain ,
- - potential,
- - normal derivative of potential,
- - Green function, also known as fundamental solution,
- - domain function