Open Collections

Local analysis for close evaluation of layer potentials

Banff International Research Station for Mathematical Innovation and Discovery

Accurate evaluation of layer potentials near boundaries and interfaces are needed in many applications, including fluid-structure interaction problems. A classical method to approximate the solution everywhere in the domain consists of using the same quadrature rule (Nyström method) used to solve the underlying boundary integral equation. This method is problematic for evaluations close to boundaries and interfaces. For a fixed number, N, of quadrature points, this method incurs a non-uniform error with O(1) errors in a boundary layer of thickness O(1/N). We have developed new asymptotic methods to remove this error. To demonstrate this method, we consider the Laplace problem and show the methods extended to the Stokes equations.

Mathematics; Numerical analysis; Partial differential equations; Women and early careers in math

video/mp4

Author affiliation: UC Merced

2020-09-12

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/75991

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/