An adaptation of the fast multipole method for evaluating layer potentials in two dimensions

5Citations
Citations of this article
2Readers
Mendeley users who have this article in their library.
Get full text

Abstract

Standard implementations of the fast multipole method, which compute fields due to point sources or dipoles, cannot be used to accurately evaluate the single- and double-layer potentials of potential theory close to the boundary, or on the boundary when the boundary curves back on itself. We describe the modifications necessary to accurately evaluate layer potentials in two dimensions, which include quadrature rules for the short-range contributions to the field, continuous multipole moments for long-range contributions, and a more complex bookkeeping procedure. We give formulae for second-, third-, and fourth-order methods. We show tests to verify the correctness of the method and numerical results which demonstrate the usefulness of the method for evaluating layer potentials near the boundary.

Cite

CITATION STYLE

APA

Mckenney, A. (1996). An adaptation of the fast multipole method for evaluating layer potentials in two dimensions. Computers and Mathematics with Applications, 31(1), 33–57. https://doi.org/10.1016/0898-1221(95)00181-W

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free