Domain Decomposition Using Spectral Expansions of Steklov-Poincaré Operators
Domain Decomposition Using Spectral Expansions of Steklov-Poincaré Operators
复制标题
使用 Steklov-Poincaré 算子的谱展开进行域分解
DOI：
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发表时间：
1995
影响因子：
3.1
通讯作者：
R. Natarajan
中科院分区：
文献类型：
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作者：
R. Natarajan
描述了一种新的域分解方法，用于解决划分为非重叠子域的区域上的椭圆边值问题，这些子域使用伽辽金有限元方法独立离散。使用独立的低维界面基函数集对解决方案提出域间连续性要求，这些基函数是通过解决互补区域上的 Steklov-Poincare 算子的特征值问题而针对每个子域单独导出的。这里针对两个子域情况描述了该方法的有效数值实现，并针对一些测试示例研究了其收敛特性。在具体示例中（涉及划分为矩形子域的矩形区域上的常系数问题），子域内部离散解的点向误差以界面模式的数量呈指数收敛，因此本方法实际上是一种直接求解方法。在其他例子中...
A new domain decomposition method is described for solving elliptic boundary value problems on a region partitioned into nonoverlapping subdomains, which are discretized independently using a Galerkin finite element method. The interdomain continuity requirements on the solution are imposed using an independent, low-dimensional set of interfacial basis functions, which are separately derived for each subdomain by solving an eigenvalue problem for the Steklov–Poincare operator on the complementary region. The efficient numerical implementation of this method is described here for the two subdomain case, and its convergence properties are studied for some test examples. In specific examples (involving constant coefficient problems on rectangular regions partitioned into rectangular subdomains), the pointwise error of the discrete solution in the subdomain interior converges exponentially in the number of interfacial modes, so that the present method is effectively a direct solution method. In other examples...