A Solver for Helmholtz System Generated by the Discretization of Wave Shape Functions
A Solver for Helmholtz System Generated by the Discretization of Wave Shape Functions
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DOI：
10.1017/s2070073300001235
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发表时间：
2013-12
影响因子：
1.4
通讯作者：
Long Yuan;Q. Hu
中科院分区：
文献类型：
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作者：
Long Yuan;Q. Hu
B. Despres [1] 中介绍了一种有趣的亥姆霍兹方程离散化方法。该方法基于超弱变分公式 (UWVF) 和波形函数，它们是控制亥姆霍兹方程的精确解。在本文中，我们关注的是由[1]中的方法生成的系统的快速求解器。我们为此类系统提出了一种新的预处理器，它可以被视为粗略求解器和[13]中引入的块对角预处理器之间的组合。在我们的数值实验中，该预处理器被应用于求解二维和三维亥姆霍兹方程，数值结果表明新的预处理器比原始的块对角预处理器更有效。
An interesting discretization method for Helmholtz equations was introduced in B. Despres [1]. This method is based on the ultra weak variational formulation (UWVF) and the wave shape functions, which are exact solutions of the governing Helmholtz equation. In this paper we are concerned with fast solver for the system generated by the method in [1]. We propose a new preconditioner for such system, which can be viewed as a combination between a coarse solver and the block diagonal preconditioner introduced in [13]. In our numerical experiments, this preconditioner is applied to solve both two-dimensional and three-dimensional Helmholtz equations, and the numerical results illustrate that the new preconditioner is much more efficient than the original block diagonal preconditioner.