https://hal.science/hal-01530928v1Carvalho, CamilleCamilleCarvalhoUC Merced - University of California [Merced] - UC - University of CaliforniaKhatri, ShilpaShilpaKhatriUC Merced - University of California [Merced] - UC - University of CaliforniaKim, ArnoldArnoldKimUC Merced - University of California [Merced] - UC - University of CaliforniaAsymptotic analysis for close evaluation of layer potentialsHAL CCSD2018Boundary integral equationsLaplace's equationLayer potentialsNearly singular integralsClose evaluations[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA][MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph][MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]Carvalho, Camille2017-06-01 02:22:042022-11-29 12:04:082017-06-07 11:40:36enJournal articleshttps://hal.science/hal-01530928v1application/pdf1Accurate evaluation of layer potentials near boundaries is needed in many applications, including fluid-structure interactions and near-field scattering in nano-optics. When numerically evaluating layer potentials, it is natural to use the same quadrature rule as the one used in the NystrÃ¶m method to solve the underlying boundary integral equation. However, this method is problematic for evaluation points close to boundaries. For a fixed number of quadrature points, N , this method incurs O(1) errors in a boundary layer of thickness O(1/N). Using an asymp-totic expansion for the kernel of the layer potential, we remove this O(1) error. We demonstrate the effectiveness of this method for interior and exterior problems for Laplace's equation in two dimensions.