科研之友
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摘要
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(3/2)log(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.
- 出版日期2012-10
- 单位中国科学院数学与系统科学研究院
