Fast Calderón preconditioning for Helmholtz boundary integral equations

Ignacia Fierro, Carlos Jerez-Hanckes

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Calderón multiplicative preconditioners are an effective way to improve the condition number of first kind boundary integral equations yielding provable mesh independent bounds. However, when discretizing by local low-order basis functions as in standard Galerkin boundary element methods, their computational performance worsens as meshes are refined. This stems from the barycentric mesh refinement used to construct dual basis functions that guarantee the discrete stability of L2-pairings. Based on coarser quadrature rules over dual cells and H-matrix compression, we propose a family of fast preconditioners that significantly reduce assembly and computation times when compared to standard versions of Calderón preconditioning for the three-dimensional Helmholtz weakly and hyper-singular boundary integral operators. Several numerical experiments validate our claims and point towards further enhancements.

Original languageEnglish
Article number109355
JournalJournal of Computational Physics
StatePublished - 15 May 2020
Externally publishedYes


  • Boundary elements method
  • Calderón preconditioning
  • Fast solvers
  • Helmholtz equations
  • Hierarchical matrices
  • Operator preconditioning


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