A Fast Direct Solver for a Class of 3-D Elliptic Partial Differential Equation with Variable Coefficient

A Fast Direct Solver for a Class of 3-D Elliptic Partial Differential Equation with Variable Coefficient

Year:    2012

Communications in Computational Physics, Vol. 12 (2012), Iss. 4 : pp. 1148–1162

Abstract

We propose a direct solver for the three-dimensional Poisson equation with a variable coefficient, and an algorithm to directly solve the associated sparse linear systems that exploits the sparsity pattern of the coefficient matrix. Introducing some appropriate finite difference operators, we derive a second-order scheme for the solver, and then two suitable high-order compact schemes are also discussed. For a cube containing N nodes, the solver requires O(N3/2log2N) arithmetic operations and O(NlogN) memory to store the necessary information. Its efficiency is illustrated with examples, and the numerical results are analysed.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.101110.061211a

Communications in Computational Physics, Vol. 12 (2012), Iss. 4 : pp. 1148–1162

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords: