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首页> 外文期刊>Journal of Computational Physics >Preconditioning based on Calderon's formulae for periodic fast multipole methods for Helmholtz' equation
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Preconditioning based on Calderon's formulae for periodic fast multipole methods for Helmholtz' equation

机译：基于卡尔德隆公式的Helmholtz方程周期快速多极子方法的预处理

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摘要

Solution of periodic boundary value problems is of interest in various branches of science and engineering such as optics, electromagnetics and mechanics. In our previous studies we have developed a periodic fast multipole method (FMM) as a fast solver of wave problems in periodic domains. It has been found, however, that the convergence of the iterative solvers for linear equations slows down when the solutions show anomalies related to the periodicity of the problems. In this paper, we propose preconditioning schemes based on Calderon's formulae to accelerate convergence of iterative solvers in the periodic FMM for Helmholtz' equations. The proposed preconditioners can be implemented more easily than conventional ones. We present several numerical examples to test the performance of the proposed preconditioners. We show that the effectiveness of these preconditioners is definite even near anomalies.
机译：周期性边值问题的解决方案在科学和工程学的各个分支（例如光学，电磁学和力学）中都受到关注。在我们以前的研究中，我们已经开发了一种周期性快速多极子方法（FMM）作为周期域中波动问题的快速求解器。然而，已经发现，当解显示出与问题的周期性有关的异常时，线性方程的迭代解算器的收敛变慢。在本文中，我们提出了一种基于Calderon公式的预处理方案，以加快Helmholtz方程在周期FMM中迭代求解器的收敛速度。所提出的预处理器比常规预处理器更容易实现。我们提供了几个数值示例来测试所提出的预处理器的性能。我们表明，即使在异常情况下，这些预处理器的有效性也是确定的。

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