The discrete artificial boundary condition on a polygonal artificial boundary for the exterior problem of Poisson equation by using the direct method of lines
An exterior problem of the Poisson equation is investigated. A polygonal artificial boundary with a discrete artificial boundary condition on it is constructed. Then the original problem is divided into two problems connected on the artificial boundary, first with the Laplace equation on the unbounded domain and second with the Poisson equation but on the bounded domain with a polygonal boundary. The numerical solution of this second problem is obtained using the finite element approximation and it is proved that the finite element approximation problem is well posed. The numerical solution of the unbounded problem is obtained using a transformation into a semi-infinite strip problem with a discontinuous coefficient in the differential equation. Some numerical examples are included. They show that this discrete artificial boundary condition is very effective and more accurate than the Neumann boundary condition which is often used in engineering literatures.
scientific article; zbMATH DE number 1444070
scientific article