EXPERIMENTS WITH AN ORDINARY DIFFERENTIAL-EQUATION SOLVER IN THE PARALLEL SOLUTION OF METHOD OF LINES PROBLEMS ON A SHARED-MEMORY PARALLEL COMPUTER

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:38

Article; Proceedings Paper

KAHANER, DK ; NG, E ; SCHIESSER, WE ; THOMPSON, S

关键词: ORDINARY DIFFERENTIAL EQUATIONS;    ODE;    NUMERICAL ANALYSIS;    METHOD OF LINES;    MOL;    MATHEMATICAL SOFTWARE;   

DOI  :  10.1016/0377-0427(91)90173-H

来源: Elsevier

【 摘 要 】

We consider method of lines solutions of partial differential equations on shared-memory parallel computers. Solutions using the ordinary differential equation solver SDRIV3 (which is similar to the well-known LSODE solver) are considered. It is shown that portions of the solver may be implemented in parallel. In particular, formation of the Jacobian matrix and the linear algebra required to solve the corrector equations are natural candidates for parallel implementation since these portions dominate the cost of solving large systems of equations. A variant of Gaussian elimination is described which allows efficient parallel solution of systems of linear equations. An implementation of SDRIV3 which performs the Jacobian related calculations in parallel and which uses this variant of Gaussian elimination is described. The modified solver is used to solve a model hyperbolic fluid flow problem. Timing results, obtained using a Sequent Balance parallel computer, are given which demonstrate that substantial speedups are possible. Extensions of the techniques to sparse problems are discussed and illustrated for a problem involving a humidification column which contacts air and water.

【 授权许可】

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