The implicit pipeline method

We present a novel scheme for the solution of linear differential equation systems on parallel computers. The Implicit Pipeline (ImP) method uses an implicit time-integration scheme coupled with an iterative linear solver to solve the resulting differential algebraic system. The ImP method then allows for two independent mechanisms for parallelism: pipelining of the solution of several timesteps simultaneously and pipelining of the successive linear iterations in the solution of each individual time-step. Since pipelining allows for a highly structured communication pattern, it is possible to achieve good parallel performance on large processor sets. Performance results from a Cray T3E are given.