Regularized integral equations and fast high-order solvers for sound-hard acoustic scattering problems

Oscar Bruno, Tim Elling, Catalin Turc

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


This text introduces the following: (1) new regularized combined field integral equations (CFIE-R) for frequency-domain sound-hard scattering problems; and (2) fast, high-order algorithms for the numerical solution of the CFIE-R and related integral equations. Similar to the classical combined field integral equation (CFIE), the CFIE-R are uniquely-solvable integral equations based on the use of single and double layer potentials. Unlike the CFIE, however, the CFIE-R utilize a composition of the double-layer potential with a regularizing operator that gives rise to highly favorable spectral properties-thus making it possible to produce accurate solutions by means of iterative solvers in small numbers of iterations. The CFIE-R-based fast high-order integral algorithms introduced in this text enable highly accurate solution of challenging sound-hard scattering problems, including hundred-wavelength cases, in single-processor runs on present-day desktop computers. A variety of numerical results demonstrate the qualities of the numerical solvers as well as the advantages that arise from the new integral equation formulation.

Original languageEnglish (US)
Pages (from-to)1045-1072
Number of pages28
JournalInternational Journal for Numerical Methods in Engineering
Issue number10
StatePublished - Sep 7 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


  • Acoustic scattering
  • Combined field integral equations
  • Pseudo-differential operators


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