%0 Journal Article
%T Fast integral equation methods for the modified Helmholtz equation
%A Mary-Catherine Kropinski
%A Bryan Quaife
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.jcp.2010.09.030
%X We present a collection of integral equation methods for the solution to the two-dimensional, modified Helmholtz equation, $u(\x) - \alpha^2 \Delta u(\x) = 0$, in bounded or unbounded multiply-connected domains. We consider both Dirichlet and Neumann problems. We derive well-conditioned Fredholm integral equations of the second kind, which are discretized using high-order, hybrid Gauss-trapezoid rules. Our fast multipole-based iterative solution procedure requires only O(N) or $O(N\log N)$ operations, where N is the number of nodes in the discretization of the boundary. We demonstrate the performance of the methods on several numerical examples.
%U http://arxiv.org/abs/1006.0008v2