Parallel Dichotomy Algorithm for solving tridiagonal system of linear equations with multiple right-hand sides

A parallel algorithm for solving a series of matrix equations with a constant tridiagonal matrix and different right-hand sides is proposed and studied. The process of solving the problem is represented in two steps. The first preliminary step is calculating some rows of the inverse matrix of system...

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Vydané v:Parallel computing Ročník 36; číslo 8; s. 423 - 438
Hlavný autor: Terekhov, Andrew V.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.08.2010
Predmet:
Alternating direction method
Fourier method
Parallel algorithm
Poisson equation
Thomas algorithm
Tridiagonal matrix algorithm (TDMA)
Alternating direction method
Poisson equation
Parallel algorithm
Thomas algorithm
Fourier method
Tridiagonal matrix algorithm (TDMA)
ISSN:0167-8191, 1872-7336
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Popis
Shrnutí:A parallel algorithm for solving a series of matrix equations with a constant tridiagonal matrix and different right-hand sides is proposed and studied. The process of solving the problem is represented in two steps. The first preliminary step is calculating some rows of the inverse matrix of system of linear algebraic equations. The second step consists in calculating solutions for all right-hand sides. For reducing the communication interactions, based on the formulated and proved the main Gaussian Parallel Elimination Theorem for tridiagonal system of equations, we propose an original algorithm for calculating share components of the solution vector. Theoretical estimates validating the efficiency of the approach for both the common- and distributed-memory supercomputers are obtained. Direct and iterative methods of solving a 2D Poisson equation, which include procedures of tridiagonal matrix inversion, are realized using the MPI paradigm. Results of computational experiments on a multicomputer demonstrate a high efficiency and scalability of the parallel Dichotomy Algorithm.
ISSN:0167-8191
1872-7336
DOI:10.1016/j.parco.2010.02.005