Parallel solution of large‐scale differential‐algebraic systems

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Abstract
DASPK solves large‐scale systems of differential‐algebraic equations. It is based on the integration method in DASSL, but instead of a direct method for the associated linear systems which arise at each time step, the preconditioned GMRES iteration is applied in combination with an inexact Newton method. Two parallel versions of DASPK have been developed: DASPKF90, a Fortran 90 data parallel implementation, and DASPKMP, a message‐passing implementation written in Fortran 77 with extended BLAS. The parallel versions have been implemented for the Thinking Machines Corporation (TMC) CM‐5, a massively parallel multiprocessor, keeping the user interface relatively simple while allowing for portability to other massively parallel architectures. The codes have been demonstrated on several large‐scale test problems, including three‐dimensional formulations of the heat equation, the Cahn‐Hilliard equation and a multi‐species reaction‐diffusion problem. The formulations are described, including detail on preconditioning the Krylov iteration, timing results and performance analysis.

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