We present a simple high-order singularity subtraction technique for the numerical evaluation of Laplace boundary integral operators and layer potentials in two-spatial dimensions. The proposed technique allows integral operators and layer potentials to be expressed in terms of integrands of prescribed smoothness. The resulting boundary integrals can then be easily, accurately, and inexpensively evaluated by means of standard quadrature rules. The method relies on the use of Green’s third identity and a point-wise Taylor-like expansion of the density function in terms of harmonic polynomials. Numerical examples demonstrate the effectiveness of the technique when used in conjunction with the classical trapezoidal rule. Accurate numerical simulations of the electrical response of closely packed biological cells further illustrate the applicability of the proposed methodology.
C. Perez-Arancibia, L. M. Faria, C. Turc, A high-order singularity subtraction technique for the Laplace equation in the plane, submitted (arXiv preprint).
Error of method when applied to the electrical response of closely packed biological cells