Three-dimensional elliptic solvers for interface problems and applications
Three-dimensional elliptic solvers for interface problems and applications
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DOI：
10.1016/s0021-9991(02)00028-1
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发表时间：
2003-01-01
影响因子：
4.1
通讯作者：
Li, ZL
中科院分区：
文献类型：
--
作者：
Deng, SZ;Ito, K;Li, ZL
本文给出了三维界面问题的二阶精度椭圆型笛卡尔网格求解器，其中系数、源项、解及其法向通量在界面上可能是不连续的。我们的方法之一是设计用于一般的界面问题的可变，但不连续的系数。该方案使用约束优化技术保持离散最大值原理。采用代数多重网格法求解离散系统。第二种方法是针对具有分段常系数的界面问题设计的。该方法是基于快速浸入界面法和快速三维泊松求解器。第二种方法已被修改，以解决不规则区域上的Helmholtz/Poisson方程。我们的方法的形状识别的反界面问题的应用。在这个应用中，水平集方法被应用于迭代地寻找未知表面。(C)2002 Elsevier Science B. V.保留所有权利。
Second-order accurate elliptic solvers using Cartesian grids are presented for three-dimensional interface problems in which the coefficients, the source term, the solution and its normal flux may be discontinuous across an interface. One of our methods is designed for general interface problems with variable but discontinuous coefficient. The scheme preserves the discrete maximum principle using constrained optimization techniques. An algebraic multigrid solver is applied to solve the discrete system. The second method is designed for interface problems with piecewise constant coefficient. The method is based on the fast immersed interface method and a fast 3D Poisson solver. The second method has been modified to solve Helmholtz/Poisson equations on irregular domains. An application of our method to an inverse interface problem of shape identification is also presented. In this application, the level set method is applied to find the unknown surface iteratively. (C) 2002 Elsevier Science B.V. All rights reserved.