Maximum principle preserving schemes for interface problems with discontinuous coefficients
Maximum principle preserving schemes for interface problems with discontinuous coefficients
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DOI：
10.1137/s1064827500370160
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发表时间：
2001-06-27
影响因子：
3.1
通讯作者：
Ito, K
中科院分区：
文献类型：
--
作者：
Li, ZL;Ito, K
对于具有变间断系数、奇异源和非光滑甚至间断解的椭圆型界面问题，发展了一种新的笛卡尔网格有限差分方法。利用二次优化技术构造了满足离散最大值原理符号性质的新的有限差分格式。在一定条件下，使用比较函数的方法收敛。所得到的线性方程组的系数矩阵是一个M-矩阵，并与多重网格求解器耦合。数值算例表明了所提方法的有效性。
New finite difference methods using Cartesian grids are developed for elliptic interface problems with variable discontinuous coefficients, singular sources, and nonsmooth or even discontinuous solutions. The new finite difference schemes are constructed to satisfy the sign property of the discrete maximum principle using quadratic optimization techniques. The methods are shown to converge under certain conditions using comparison functions. The coefficient matrix of the resulting linear system of equations is an M-matrix and is coupled with a multigrid solver. Numerical examples are also provided to show the efficiency of the proposed methods.