In this paper, we propose a numerical formula to calculate time-harmonic electromagnetic field interacting with three-dimensional elastic body. The formula is based on the method of fundamental solutions. Firstly, we perform Helmholtz decomposition on the displacement field. The problem will transform into a coupled bounded problem including a scaler Helmholtz equation, a vector Helmholtz equation and a Maxwell equation. Then, we use the method of fundamental solutions to solve the new problem. Finally, we provide some examples to demonstrate the effectiveness of the proposed method. We construct the exact solutions for the boundary value problem to verify the accuracy and present a comparative study with the Galerkin scheme.

中文翻译：

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一种基于三维弹性体时间谐波电磁场基本解法的无网格方法


在本文中，我们提出了一个数值公式来计算与三维弹性体相互作用的时谐电磁场。该公式基于基本解决方案的方法。首先，我们在位移场上进行亥姆霍兹分解。该问题将转换为耦合有界问题，包括缩放器亥姆霍兹方程、向量亥姆霍兹方程和麦克斯韦方程。然后，我们使用基本解决方案的方法来解决新问题。最后，我们提供了一些示例来证明所提出的方法的有效性。我们构建了边界值问题的精确解以验证准确性，并提出了与 Galerkin 方案的比较研究。