Solving boundary value problems with boundary element methods requires specific Green functions suited to the boundary conditions of the problem. Using vector algebra, one often needs to use a Green function for the Helmholtz equation whereas it is a solution of the perturbed Dirac equation that is required for solving electromagnetic problems using Clifford algebra. A wealth of different Green functions of the Helmholtz equation are already documented in the literature. However, perturbed Dirac equation is only solved for the generic case and only its fundamental solution is reported. In this paper, we present a simple framework to use known Green functions of Helmholtz equation to construct the corresponding Green functions of perturbed Dirac equation which are essential in finding the appropriate kernels for integral equations of electromagnetic problems. The procedure is further demonstrated in a few examples.

中文翻译：

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利用先验已知的矢量格林函数解Clifford代数的摄动Dirac方程

用边界元方法解决边值问题需要适合问题边界条件的特定格林函数。使用矢量代数时，人们通常需要对亥姆霍兹方程使用格林函数，而这是摄动狄拉克方程的一种解决方案，这是使用克利福德代数解决电磁问题所必需的。文献中已经记录了亥姆霍兹方程的许多不同的格林函数。但是，仅在一般情况下解扰动的Dirac方程，并且只报告了其基本解。在本文中，我们提出了一个简单的框架，使用已知的亥姆霍兹方程的格林函数来构造扰动的狄拉克方程的相应格林函数，这对于寻找电磁问题积分方程的适当核至关重要。在一些示例中进一步演示了该过程。