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By Michihiro Kitahara

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K. P. , London, 1982. A. ); Recent Advances in Boundary Element Methods, Pentech Press, London, 1978. ; The Boundary Element Method for Engineers, Pentech Press, London, 1978. A. ; Boundary Element Techniques in Engineering, NewnesButterworths, London, 1980. Brebbia, CA. ); New Developments in Boundary Element Methods, Butterworths, London, 1980. Brebbia, CA. ); Boundary Element Methods, Springer-Verlag, Berlin, 1981. Brebbia, CA. ); Progress in Boundary Element Methods, Vol. 1, Pentech Press, London, 1981.

16) , where the prime in /«(·) and Hnv'(·) denotes the differentiation with respect to the argument. 2 Integration of the double layer potential The double layer potential generated by the density ψ on the circle is defined as -58- ny / 3D {Τυ(Χ,ν;ω)\ψ(ν)α5« = [ \μ-£-υ(Χ,υ,ω)]φΙυ)α8» J 3D[ any =- f ·> *D \ {ßVxU(X,v\w)-n{y)(l>(y)dsv. 17) The Fourier transform of this potential is ϋ(ξ) = μΡαξ)-'(ίξ)· f e-iiyn(y)

These rela­ tions are still valid for the integral equations with an arbitrary geometry; the explicit relations for the special shaped geometry will be considered in the next chapter. Secondly, it is to be remarked that we have formulated the "boundary" integral equa­ tions in the last chapter. In this case, eigenparameter ω (angular frequency) is contained in the integral kernel, for example, as an argument of the Hankel function in the twodimensional problem. Alternatively, if we formulate the integral equation concerned with the volume potential, eigenparameter ω is out of the integral sign.

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