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A higher-order compact method in space and time based on parallel implementation of the Thomas algorithm. (English) Zbl 0959.65102

The authors propose a method to parallelize high-order compact numerical algorithms for the solution of three-dimensional partial differential equations in a space-time domain. This method is compared with the basic pipelined Thomas algorithm. In the proposed algorithm, the processors are used for the next computational tasks, whereas in the basic pipelined Thomas algorithm they stay idle waiting for the data from neighboring processors at the forward and the backward steps of the Thomas algorithm.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
35L45 Initial value problems for first-order hyperbolic systems
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