Artificial Boundary Conditions for linear and nonlinear Schroedinger equations
06 February 2009
Dr Ehrhardt Matthias
Weierstrass Institute for Applied Analysis and Stochastics, Germany
Applied Mathematics, Computational Mathematics Physics and Astronomy
Condensed Matter Physics
When computing numerically the solution of a linear or nonlinear partial differential equation in an unbounded domain, a fictitious boundary are usually introduced to limit the computational domain. Special boundary conditions are derived at this boundary to approximate the exact whole-space solution. If the solution of the problem on the bounded domain is equal to the whole-space solution (restricted to the computational domain) these boundary conditions are called exact or transparent boundary conditions (TBCs), otherwise they are called artificial boundary conditions (ABCs). Different strategies can therefore be developed.