@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 = {<p style="text-align: justify;">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(N<sup>3/2</sup>log<sup>2</sup>N) arithmetic operations
and O(NlogN) memory to store the necessary information. Its efficiency is illustrated
with examples, and the numerical results are analysed.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.101110.061211a},
url = {http://global-sci.org/intro/article_detail/cicp/7329.html}
}