TY - JOUR
T1 - A local target specific quadrature by expansion method for evaluation of layer potentials in 3D
AU - Siegel, Michael
AU - Tornberg, Anna Karin
N1 - Funding Information:
This work has been supported by the Knut and Alice Wallenberg Foundation under grant No. KAW2014.0338 and is gratefully acknowledged. The authors also gratefully acknowledge support by the Göran Gustafsson Foundation for Research in the Natural Sciences (A.K.T.), and the National Science Foundation grant DMS-1412789 (M.S.).
Funding Information:
This work has been supported by the Knut and Alice Wallenberg Foundation under grant No. KAW2014.0338 and is gratefully acknowledged. The authors also gratefully acknowledge support by the Göran Gustafsson Foundation for Research in the Natural Sciences (A.K.T.), and the National Science Foundation grant DMS-1412789 (M.S.).
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - Accurate evaluation of layer potentials is crucial when boundary integral equation methods are used to solve partial differential equations. Quadrature by expansion (QBX) is a recently introduced method that can offer high accuracy for singular and nearly singular integrals, using truncated expansions to locally represent the potential. The QBX method is typically based on a spherical harmonics expansion which when truncated at order p has O(p2) terms. This expansion can equivalently be written with p terms, however paying the price that the expansion coefficients will depend on the evaluation/target point. Based on this observation, we develop a target specific QBX method, and apply it to Laplace's equation on multiply-connected domains. The method is local in that the QBX expansions only involve information from a neighborhood of the target point. An analysis of the truncation error in the QBX expansions is presented, practical parameter choices are discussed and the method is validated and tested on various problems.
AB - Accurate evaluation of layer potentials is crucial when boundary integral equation methods are used to solve partial differential equations. Quadrature by expansion (QBX) is a recently introduced method that can offer high accuracy for singular and nearly singular integrals, using truncated expansions to locally represent the potential. The QBX method is typically based on a spherical harmonics expansion which when truncated at order p has O(p2) terms. This expansion can equivalently be written with p terms, however paying the price that the expansion coefficients will depend on the evaluation/target point. Based on this observation, we develop a target specific QBX method, and apply it to Laplace's equation on multiply-connected domains. The method is local in that the QBX expansions only involve information from a neighborhood of the target point. An analysis of the truncation error in the QBX expansions is presented, practical parameter choices are discussed and the method is validated and tested on various problems.
KW - Exterior Dirichlet problem
KW - Integral equations
KW - Layer potentials
KW - Multiply-connected domain
KW - Quadrature by expansion
KW - Spherical harmonics expansions
UR - http://www.scopus.com/inward/record.url?scp=85044166752&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85044166752&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2018.03.006
DO - 10.1016/j.jcp.2018.03.006
M3 - Article
AN - SCOPUS:85044166752
SN - 0021-9991
VL - 364
SP - 365
EP - 392
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -