Volume 12, Issue 4
A Fast Direct Solver for a Class of 3-D Elliptic Partial Differential Equation with Variable Coefficient

Beibei Huang, Bin Tu & Benzhuo Lu

Commun. Comput. Phys., 12 (2012), pp. 1148-1162.

Published online: 2012-12

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  • 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 andO(NlogN) memory to store the necessary information. Its efficiency is illustrated with examples, and the numerical results are analysed. 

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@Article{CiCP-12-1148, author = {Beibei Huang, Bin Tu and Benzhuo Lu}, title = {A Fast Direct Solver for a Class of 3-D Elliptic Partial Differential Equation with Variable Coefficient}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {4}, pages = {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 andO(NlogN) memory to store the necessary information. Its efficiency is illustrated with examples, and the numerical results are analysed. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.101110.061211a}, url = {http://global-sci.org/intro/article_detail/cicp/7329.html} }
TY - JOUR T1 - A Fast Direct Solver for a Class of 3-D Elliptic Partial Differential Equation with Variable Coefficient AU - Beibei Huang, Bin Tu & Benzhuo Lu JO - Communications in Computational Physics VL - 4 SP - 1148 EP - 1162 PY - 2012 DA - 2012/12 SN - 12 DO - http://dor.org/10.4208/cicp.101110.061211a UR - https://global-sci.org/intro/cicp/7329.html KW - AB -

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 andO(NlogN) memory to store the necessary information. Its efficiency is illustrated with examples, and the numerical results are analysed. 

Beibei Huang, Bin Tu & Benzhuo Lu. (1970). A Fast Direct Solver for a Class of 3-D Elliptic Partial Differential Equation with Variable Coefficient. Communications in Computational Physics. 12 (4). 1148-1162. doi:10.4208/cicp.101110.061211a
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