%0 Journal Article
%T Asymptotic analysis for close evaluation of layer potentials
%+ University of California [Merced] (UC Merced)
%A Carvalho, Camille
%A Khatri, Shilpa
%A Kim, Arnold, D
%< avec comitÃ© de lecture
%@ 0021-9991
%J Journal of Computational Physics
%I Elsevier
%8 2018
%D 2018
%K Boundary integral equations
%K Laplace's equation
%K Layer potentials
%K Nearly singular integrals
%K Close evaluations
%Z Mathematics [math]/Numerical Analysis [math.NA]
%Z Mathematics [math]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles
%X Accurate 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.
%G English
%2 https://hal.science/hal-01530928v1/document
%2 https://hal.science/hal-01530928v1/file/CKK-2017.pdf
%L hal-01530928
%U https://hal.science/hal-01530928