General-purpose kernel regularization of boundary integral equations via density interpolation

This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calderón calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density interpolation methods, the proposed relies on interpolating function around singularity terms solutions underlying homogeneous PDE, so as recast singular nearly integrals bounded (or more regular) integrands. We present here simple strategy which, unlike approaches, does not entail explicit computation derivatives along surface. Furthermore, approach is kernel- dimension-independent sense that sought interpolant constructed combination point-source fields, given by same Green’s used equation formulation, thus making procedure applicable, principle, any PDE known function. For sake definiteness, we focus Nystr‘?om methods for (scalar) Laplace Helmholtz equations (vector) elastostatic time-harmonic elastodynamic equations. The method’s accuracy, flexibility, efficiency, compatibility fast solvers are demonstrated means variety large-scale three-dimensional numerical examples.