摘要
Boundary integral methods are naturally suited for the computation of harmonic functions on a region having inclusions or cells with different material properties.However,accuracy deteriorates when the cell boundaries are close to each other.We present a boundary integralmethod in two dimensions which is specially designed tomaintain second order accuracy even if boundaries are arbitrarily close.Themethod uses a regularization of the integral kernel which admits analytically determined corrections to maintain accuracy.For boundaries with many components we use the fast multipolemethod for efficient summation.We compute electric potentials on a domain with cells whose conductivity differs from that of the surrounding medium.We first solve an integral equation for a source term on the cell interfaces and then find values of the potential near the interfaces via integrals.Finally we use a Poisson solver to extend the potential to a regular grid covering the entire region.A number of examples are presented.We demonstrate that increased refinement is not needed to maintain accuracy as interfaces become very close.
