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 coeff...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(NlogN)memory to store the necessary information.Its efficiency is illustrated with examples,and the numerical results are analysed.展开更多
基金supported by NFS No.11001257,was stimulated by Per-Gunnar Martinsson’s paper”A Fast Direct Solver for a Class of Elliptic Partial Differential Equations”.Professor Jingfang Huang suggested solving the Poisson equation with variable coefficient as a test case.We are very grateful to both of them for their selfless help.
文摘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(NlogN)memory to store the necessary information.Its efficiency is illustrated with examples,and the numerical results are analysed.
