A local target specific quadrature by expansion method for evaluation of layer potentials in 3D

Michael Siegel, Anna Karin Tornberg

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)365-392
Number of pages28
JournalJournal of Computational Physics
StatePublished - Jul 1 2018

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Exterior Dirichlet problem
  • Integral equations
  • Layer potentials
  • Multiply-connected domain
  • Quadrature by expansion
  • Spherical harmonics expansions


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