Solution of Poisson's Equations on Infinite Domains
One nice application of domain decomposition techniques is that they can be employed to construct solutions of
Poisson's equation in infinite domains. Essentially, the idea is to glue together a computational (e.g. grid based)
solution for the computational region of interest with an analytic solution for the "far field". This
procedure is described in the paper "Domain Decomposition Techniques and the Solution of Poisson's
Equation in Infinite Domains".
"Domain Decomposition Techniques and the Solution of Poisson's
Equation in Infinite Domains", Christopher R. Anderson, Domain Decomposition Methods, Proceedings
of the Second International Symposium on Domain Decomposition, Los Angeles, 1988. T. Chan, R. Glowinski, J. Periaux,
O. Widlund, eds., SIAM publications, 1988. pg. 129-139.
Abstract : We discuss how to domain decomposition ideas can be used
to construct efficient methods for solving Poisson's equation in domains of infinite extent. We give the details
for the construction of methods to solve Poisson's equation in the region external to a circular cylinder and for
an infinite backstep. Computational results are presented.