WIAS Preprint No. 415, (1998)

Direct Linear Solvers for Vector and Parallel Computers


  • Grund, Friedrich

2010 Mathematics Subject Classification

  • 65F05 65F50 65Y05 80A30 92E20


  • Gaussian elimination, Sparse-matrix techniques, Vectorization, Parallelization, Chemical process simulation


We consider direct methods for the numerical solution of linear systems with unsymmetric sparse matrices. Different strategies for the determination of the pivots are studied. For solving several linear systems with the same pattern structure we generate a pseudo code, that can be interpreted repeatedly to compute the solutions of these systems. The pseudo code can be advantageously adapted to vector and parallel computers. For that we have to find out the instructions of the pseudo code which are independent of each other. Based on this information, one can determine vector instructions for the pseudo code operations (vectorization) or spread the operations among different processors (parallelization). The methods are successfully used on vector and parallel computers for the circuit simulation of VLSI circuits as well as for the dynamic process simulation of complex chemical production plants.

Appeared in

  • Jose M. L. M. Palma, Jack Dongarra and Vicente Hernandez, editors: Vector and Parallel Processing - VECPAR'98, Third International Conference, Porto, Portugal, June 1998, volume 1573 of Lecture Notes in Computer Science, pages 114-127. Springer-Verlag Berlin Heidelberg New York, 1999

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