An integral equation method is one of a practical numerical method for the analysis of wave problems with inhomogeneous medium. In this method, an integral equation is discretized into a linear system of equation by means of an element integration. Richmond proposed an approximation formula for an integration on a square element in two-dimensional problem. This approximation formula realized a fast computation of the integration but is unsuitable for wave analysis with high accuracy and definition. This paper presents a computational technique with the lowest operational costs for an accurate integration on the square element. We express an integration point in the two-dimensional polar coordinate system and reduce the double integral to a single one. Numerical experiments disclose a relationship between the number of abscissas for numerical quadrature and the accuracy of the computation for the square element integration. We consequently realize an accurate integration on the square element with the lowest computational costs.

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