Location of Repository

Condition number estimates for combined potential boundary integral operators in acoustic scattering

By Simon Neil Chandler-Wilde, Ivan G Graham, Stephen Langdon and Marko Lindner


We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators

Topics: 518
Publisher: Rocky Mountain Mathematics Consortium
Year: 2009
OAI identifier: oai:centaur.reading.ac.uk:1615

Suggested articles



  1. (2007). A Galerkin boundary element method for high frequency scattering by convex polygons, doi
  2. (2007). A hybrid numericalasymptotic boundary integral method for high-frequency acoustic scattering,
  3. (2007). A refined Galerkin error and stability analysis for highly indefinite variational problems,
  4. (1944). A Treatise on the Theory of Bessel Functions, doi
  5. (1992). Acoustic and Electromagnetic Scattering Theory,
  6. (1993). Boundary integral solution of the exterior acoustic problem,
  7. (1996). Boundary value problems and Hardy spaces associated to the Helmholtz equation in Lipschitz domains,
  8. (1977). Classical Banach Spaces I, SpringerVerlag,
  9. Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation, in preparation.
  10. (1999). Convergence of moment-method solutions of the electric field integral equation for a 2-D open cavity, doi
  11. (2004). Error analysis of the moment method,
  12. (1983). Integral equation methods in scattering theory,
  13. (1984). Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains,
  14. (1982). Linear Integral Operators,
  15. (1985). Minimizing the condition number of boundary integral-operators in acoustic and electromagnetic scattering,
  16. (2006). On the acoustic single layer potential: Stabilisation and Fourier analysis,
  17. (1990). On the choice of the coupling parameter in boundary integral equation formulations of the exterior acoustic problem,
  18. (1983). On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation,
  19. (1965). On the question of the solvability of the exterior boundary-value problems for the wave eqaution and Maxwell’s equations,
  20. (2001). On the spectrum of the electric field integral equation and the convergence of the moment method, doi
  21. (1978). Potential techniques for boundary value problems on C1 domains”,
  22. (2007). Private communication,
  23. (2006). Quadrature methods for multivariate highly oscillatory integrals using derivatives.
  24. (1997). Schnelle Summationsverfahren zur numerischen Lo¨sung von Integralgleichungen fu¨r Streuprobleme im R3,
  25. (2000). Strongly Elliptic Systems and Boundary Integral Equations,
  26. (2001). Surface scattering in three dimensions: an accelerated high-order solver,
  27. (1973). Tables of Laplace Transforms,
  28. (1971). The application of integral equation methods for the numerical solution of boundary value problems, doi
  29. (1965). U¨ber das Dirichletsche Außenraumproblem fu¨r die Helmholtzsche Schwingungsgleichung,
  30. (2004). Uniqueness in inverse obstacle scattering with conductive boundary conditions,
  31. (2008). Wave-number-explicit bounds in timeharmonic scattering, doi
  32. (1997). Wavelets: Caldero´n-Zygmund and Multilinear Operators,
  33. (1965). Zur Dirichtletschen Randwertaufgabe des Aussenraums der Schwingungsgleichung,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.