@Article{CiCP-12-1148, author = {}, 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 and O(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} }