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A dual-level method of fundamental solutions for three-dimensional exterior high frequency acoustic problems

机译：三维外部高频声学问题基本解的双层方法

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Physical essence of the fictitious boundary of the method of fundamental solutions has been a mystery for a long time. In this study, we attempt to explain the reason why fictitious boundary has such a dramatic effect on numerical results. The influence law of the fictitious boundary on numerical results is revealed. Based on this understanding, a dual-level method of fundamental solutions with self-adaptive adjustment coefficients is proposed. The competitive attributes of the method are that it inherits the high numerical efficiency of the method of fundamental solutions, and it improves numerical stability significantly. The effect of the fictitious boundary on numerical results is eliminated by introducing the concept of equivalent slope. It should be noted that the dual-level method of fundamental solutions can simulate exterior high frequency acoustic problems under the lowest sampling frequency allowed by the Shannon's sampling theorem. Numerical experiment with up to non-dimensional wavenumber of 600 has successfully been conducted on a single laptop when one uses 100,000 degrees of freedom. (C) 2018 Elsevier Inc. All rights reserved.
机译：基本解决方案方法的虚拟边界的物理本质已经是一个谜。在本研究中，我们试图解释虚拟边界对数值结果产生如此巨大影响的原因。揭示了虚拟边界对数值结果的影响规律。在此基础上，提出了具有自适应调整系数的基本解的双层方法。该方法的竞争特性是，它继承了基本解方法的高数值效率，并且显着提高了数值稳定性。通过引入等效斜率的概念，消除了虚拟边界对数值结果的影响。应当指出，基本解的双层方法可以在香农采样定理允许的最低采样频率下模拟外部高频声学问题。当一台笔记本电脑使用100,000自由度时，在一台笔记本电脑上成功进行了高达600的无量纲波数的数值实验。 （C）2018 Elsevier Inc.保留所有权利。

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