A Domain-Decomposed Fast Poisson Solver on a Rectangle
Tony Fan-Cheong Chan, Diana C. Resasco · SIAM Journal on Scientific and Statistical Computing · 1987
We present a new domain decomposed fast Poisson solver on a rectangle divided into parallel strips or boxes. The method first performs uncoupled fast solves on each subdomain, and then the interface variables are computed exactly by Fast Fourier Transform, without computing or inverting the capacitance matrix explicitly. Finally, the solution on the interior of the subdomains can be computed by one more fast solve on each subdomain. This method is especially suited for parallel implementation, since the independent problems in the subdomains can be solved in parallel, and the communication involves the interface variables only.