Boundary Element Method

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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