A comparison among four direct boundary integral methods

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Abstract
Four distinct direct boundary integral equation (BIE) schemes, two of which are new, are derived and are used to solve multibody scattering problems. These schemes are similar in that each is a composite of integral operators that are completely continuous and are dissimilar in that they are either a mixture of equations of the first and second kind or are strictly of the second kind. Their relative usefulness is determined by analysis and numerical experiments, suggesting that the optimal scheme is governed by the tradeoff between stability and computational efficiency. To partially verify these BIE methods each was used to compute the scattering from a cylindrical obstacle and results of each method were compared to the analytic solution. In addition, one of these schemes was used to calculate the line source responses to half-space and two-layer models. The numerical and analytic solutions are in favorable agreement.

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