HAL CCSD
Asymptotic analysis for close evaluation of layer potentials
Carvalho, Camille
Khatri, Shilpa
Kim, Arnold,
University of California [Merced] (UC Merced) ; University of California (UC)
International audience
ISSN: 0021-9991
EISSN: 1090-2716
Journal of Computational Physics
Elsevier
hal-01530928
https://hal.science/hal-01530928
https://hal.science/hal-01530928v1/document
https://hal.science/hal-01530928v1/file/CKK-2017.pdf
https://hal.science/hal-01530928
Journal of Computational Physics, 2018
en
Boundary integral equations
Laplace's equation
Layer potentials
Nearly singular integrals
Close 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]
info:eu-repo/semantics/article
Journal articles
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
info:eu-repo/semantics/OpenAccess