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Application of finite elements to the solution of Helmholtz's equation

机译：有限元在亥姆霍兹方程解中的应用

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摘要

A novel method, that of finite elements, for the solution of Helmholtz's equation is suggested. Various 2- and 3-dimensional problems are solved using this method, and the results are compared with more conventional techniques, particularly the finite-difference method, which it may be regarded to supersede. The ease with which various boundary conditions may be handled is discussed and illustrated. Nonhomogeneous configurations present no difficulty, nor do they require any special formulation. There is considerable scope for the further development of the technique, which has, until now, been applied mainly to the solution of Laplace or Poisson equations.
机译：提出了一种新的有限元方法，用于求解亥姆霍兹方程。使用此方法可解决各种二维和三维问题，并将结果与​​更常规的技术（尤其是有限差分法）相比较，后者可能会被取代。讨论和说明了处理各种边界条件的难易程度。非均一的构型没有困难，也不需要任何特殊的公式。该技术的进一步发展具有很大的范围，迄今为止，该技术主要应用于拉普拉斯或泊松方程的求解。

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