On structure preserving and circulant preconditioners for the space fractional coupled nonlinear Schrodinger equations
On structure preserving and circulant preconditioners for the space fractional coupled nonlinear Schrodinger equations
复制标题
空间分数耦合非线性薛定谔方程的结构保持和循环预处理器
DOI：
10.1002/nla.2159
复制
发表时间：
2018
影响因子：
4.3
通讯作者：
Wang Dong-Ling
中科院分区：
文献类型：
--
作者：
Wang Jun-Gang;Ran Yu-Hong;Wang Dong-Ling
采用分数阶中心差分格式的隐式守恒型差分格式离散空间分数阶耦合非线性薛定谔方程组时，在每一时间步内都需要求解一个复对称线性方程组。系数矩阵的真实的部分是对称的Toeplitz-plus-diagonal矩阵，而虚部是单位矩阵。本文针对这类Toeplitz-like矩阵提出了一个保结构预条件子和一个循环预条件子。从理论上导出了预条件矩阵特征值的紧界。数值计算表明，Krylov子空间迭代方法，如BiCGSTAB，当加速所提出的预处理器，是有效的求解离散线性系统。
When the implicit, conservative difference scheme with the fractional centered difference formula is employed to discretize the space fractional coupled nonlinear Schrödinger equations, in each time step, we need to solve a complex symmetric linear system. The real part of the coefficient matrix is a symmetric Toeplitz‐plus‐diagonal matrix, whereas the imaginary part is the identity matrix. In this paper, a structure preserving preconditioner and a circulant preconditioner are proposed for such Toeplitz‐like matrix. Theoretically, tight bounds for eigenvalues of the preconditioned matrices are derived. Numerical implementations show that Krylov subspace iteration methods such as BiCGSTAB, when accelerated by the proposed preconditioners, are efficient solvers for solving the discretized linear system.