A scalable parallel Poisson solver in three dimensions with infinite-domain boundary conditions

The authors presented an elliptic free space solver that offers vastly improved performance over a previous variant of the algorithm. Processors of an IBM SP system were currently scaled up to 1024, and it is planned to port the solver to Blue Gene/L. The solver employs a method of local corrections that avoids the need for costly communication, while retaining parallel scalability of the method. Communication costs are generally small: 25 percent of the total running time or less for runs on up to 512 processors and 37 percent of the total time on 1024 processors. The numerical overheads incurred are independent of the number of processors for a wide range of problem sizes. The solver currently handles infinite-domain (free space) boundary conditions, but may be reformulated to accommodate other kinds of boundary conditions as well.