Solving Fredholm second-kind integral equations with singular right-hand sides on non-smooth boundaries

Johan Helsing, Shidong Jiang

Research output: Contribution to journalArticlepeer-review

Abstract

A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which builds on recursively compressed inverse preconditioning (RCIP), is universal as it is independent of the nature of the singularities. Strong right-hand-side singularities, such as 1/|r|α with α close to 1, can be treated in full machine precision. Adaptive refinement is used only in the recursive construction of the preconditioner, leading to an optimal number of discretization points and superior stability in the solve phase. The performance of the scheme is illustrated via several numerical examples, including an application to an integral equation derived from the linearized BGKW kinetic equation for the steady Couette flow.

Original languageEnglish (US)
Article number110714
JournalJournal of Computational Physics
Volume448
DOIs
StatePublished - Jan 1 2022

ASJC Scopus subject areas

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

Keywords

  • Integral equation method
  • Linearized BGKW equation
  • Non-smooth domain
  • RCIP method
  • Singular right-hand side

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