TY - JOUR
T1 - A fast direct solver for a class of 3-D elliptic partial differential equation with variable coefficient
AU - Huang, Beibei
AU - Tu, Bin
AU - Lu, Benzhuo
PY - 2012/10
Y1 - 2012/10
N2 - 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 3/2log 2 N) arithmetic operations and O(N log N) memory to store the necessary information. Its efficiency is illustrated with examples, and the numerical results are analysed.
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(N 3/2log 2 N) arithmetic operations and O(N log N) memory to store the necessary information. Its efficiency is illustrated with examples, and the numerical results are analysed.
KW - Direct method
KW - Discrete laplace operator
KW - Fast matrix inversion
KW - Fast solver
UR - http://www.scopus.com/inward/record.url?scp=84860676559&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84860676559&partnerID=8YFLogxK
U2 - 10.4208/cicp.101110.061211a
DO - 10.4208/cicp.101110.061211a
M3 - Article
AN - SCOPUS:84860676559
SN - 1815-2406
VL - 12
SP - 1148
EP - 1162
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 4
ER -