The Newton waveform relaxation approach to the solution of differential algebraic systems for circuit simulation
Pipelined successive overrelaxation
Parallel supercomputing: methods, algorithms and applications
Scientific Computing and Differential Equations: An Introduction to Numerical Methods
Scientific Computing and Differential Equations: An Introduction to Numerical Methods
Solving Linear Systems on Vector and Shared Memory Computers
Solving Linear Systems on Vector and Shared Memory Computers
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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 pattem, it is possible to achieve good parallel performance on large processor sets. Performance results from a Cray T3E are given.