High-order finite element–integral equation coupling on embedded meshes

Natalie N. Beams, Andreas Klöckner, Luke N. Olson

Research output: Contribution to journalArticlepeer-review


This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or inhomogeneous jump conditions without modification and retains high-order convergence close to the embedded interface. We present finite element–integral equation (FE–IE) formulations for interior, exterior, and interface problems. The treatments of the exterior and interface problems are new. The resulting linear systems are solved through an iterative approach exploiting the second-kind nature of the IE operator combined with algebraic multigrid preconditioning for the FE part. Assuming smooth continuations of coefficients and right-hand-side data, we show error analysis supporting high-order accuracy. Numerical evidence further supports our claims of efficiency and high-order accuracy for smooth data.

Original languageEnglish (US)
Pages (from-to)1295-1313
Number of pages19
JournalJournal of Computational Physics
StatePublished - Dec 15 2018
Externally publishedYes


  • Algebraic multigrid
  • FEM–IE coupling
  • Fictitious domain
  • Interface problem
  • Iterative methods
  • Layer potential

ASJC Scopus subject areas

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


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