TY - JOUR T1 - A Fast Direct Solver for a Class of 3-D Elliptic Partial Differential Equation with Variable Coefficient 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 -

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.