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Accurate evaluation of nearly singular integrals plays an important role inmany boundary integral equation based numerical methods. In this paper, wepropose a variant of singularity swapping method to accurately evaluate thelayer potentials for arbitrarily close targets. Our method is based on theglobal trapezoidal rule and trigonometric interpolation, resulting in anexplicit quadrature formula. The method achieves spectral accuracy for nearlysingular integrals on closed analytic curves. In order to extract thesingularity from the complexified distance function, an efficient root findingmethod is proposed based on contour integration. Through the change ofvariables, we also extend the quadrature method to integrals on the piecewiseanalytic curves. Numerical examples for Laplace's and Helmholtz equations showthat high order accuracy can be achieved for arbitrarily close fieldevaluation.

Singularity swapping method for nearly singular integrals based on trapezoidal rule