The w‐plane finite element method for the solution of the steady‐state scalar wave equation in two dimensions

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Abstract
A novel finite element method has been described in this paper for the solution of the steady‐state scalar wave equation in two dimensions. In this method the physical domain of the problem is mapped into an image domain; the governing equation and the prescribed boundary conditions are also appropriately transformed. Because logarithmic mapping functions are used, the physical domain is logarithmically condensed in the image plane. The method is therefore particularly suitable for the efficient and economical solution of large or very large aspect ratio problems.The high degree of accuracy which the method is capable of is demonstrated by means of two typical examples. Possible extension of the method to complex problems including non‐linearity, multiplicity, etc. is also discussed.

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