hal-01530928
https://hal.science/hal-01530928
https://hal.science/hal-01530928v1/document
https://hal.science/hal-01530928v1/file/CKK-2017.pdf
Asymptotic analysis for close evaluation of layer potentials
Carvalho, Camille
Khatri, Shilpa
Kim, Arnold,
[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]
ART
Boundary integral equations
Laplace's equation
Layer potentials
Nearly singular integrals
Close evaluations
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.
2018
2017-06-01
en
Journal of Computational Physics
Elsevier