Bi-CGSTAB for collocation equations on distributed memory parallel architectures

E. N. Mathioudakis, E. P. Papadopoulou and Y. G. Saridakis
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E. N. Mathioudakis: Technical University of Crete, Applied Mathematics and Computers Laboratory, Department of Sciences
E. P. Papadopoulou: Technical University of Crete, Applied Mathematics and Computers Laboratory, Department of Sciences
Y. G. Saridakis: Technical University of Crete, Applied Mathematics and Computers Laboratory, Department of Sciences

A chapter in Numerical Mathematics and Advanced Applications, 2003, pp 957-966 from Springer

Abstract: Summary In this paper, which extends and concludes our work in [3, 4], we deal with the problem of efficiently organizing the computation involved in the bi-conjugate gradient stabilized [5] iterative solution of large linear systems, in order to compute on a distributed memory parallel computer. These linear systems are associated with the discreti zation of elliptic boundary value problems using a collocation finite element method based on Hermite bi-cubic elements. The organization of the computation involved follows the methodology used in [3,4]. That is, having the collocation matrix in its normal 2-cyclic or red-black form for increased scalability, we map the computation involved on an appropriate virtual architecture which, in the sequel, is optimally repartitioned and mapped on to a fixed size architecture. The whole process leads to the development of an efficient and well-structured parallel algorithm. For demonstration purposes the algorithm was realized on a distributed memory Parsytee Cognitive computer CC-2.

Date: 2003
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DOI: 10.1007/978-88-470-2089-4_87

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