Transparent Boundary Conditions Based on the Pole Condition

Abstract

Transparent boundary conditions for polygonal two-dimensional domains based on the pole condition approach are presented. The discretization of the exterior is done by innite trapezoids, which allows to dene a generalized distance variable. Taking the Laplace transform of the solution w.r.t the distance variable, incoming and outgoing solutions can be distinguished by the location of the singularities. Using special ansatz and test functions, the condition on the location of the singularities yields a new algorithmic realization of transparent boundary conditions.