The waveform relaxation method in the concurrent dynamic process simulation

Abstract

We investigate the concurrent solution of low-index differential-algebraic equations (DAEas) by the waveform relaxation (WR) method, an iterative method for system integration. The WR method (or Picard—Lindelöf iteration) is an operator-splitting approach to the solution of a system of DAEs partitioned into several lower-order systems (subsystems). Such a method, when efficiently implemented, results in algorithms with a highly parallelizable concurrent fraction and low sequential overhead, making them especially suitable for coarse- and medium-grain MIMD distributed-memory machines. Since problems represented by DAEs cannot be “scaled”, our performance measure is reduction in solution time for fixed problems, and the Amdahl's-law bottleneck therefore concerns us. We describe our new simulation code DAWRS (Differential—Algebraic—Waveform Relaxation Solver), written in C, to solve DAEs on parallel machines using the WR methods. We discuss the system partitioning, and describe new techniques to improve both the local and global convergence of such methods. We demonstrate the achievable concurrent performance when solving DAEs for a class of dynamic simulation applications of chemical engineering.