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://doi.org/10.4208/cicp.101110.061211a
UR - https://global-sci.org/intro/article_detail/cicp/7329.html
KW - 
AB - <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>