Advertisement

Exterior Dirichlet and Neumann Problems for the Helmholtz Equation as Limits of Transmission Problems

  • M.-L. Rapún
  • F.-J. Sayas

Keywords

Dirichlet Problem Boundary Element Method Neumann Problem Boundary Integral Equation Helmholtz Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AH01]
    Atkinson, K., Han, W.: Theoretical Numerical Analysis: A Functional Analysis Framework. Springer, New York (2001).MATHGoogle Scholar
  2. [CZ92]
    Chen, G., Zhou, J.: Boundary Element Methods. Academic Press, London (1992).MATHGoogle Scholar
  3. [CK83]
    Colton, D.L., Kress, R.: Integral Equation Methods in Scattering Theory. Wiley, New York (1983).MATHGoogle Scholar
  4. [CS85]
    Costabel, M., Stephan, E.: A direct boundary integral equation method for transmission problems. J. Math. Anal. Appl., 106, 367–413 (1985).MATHCrossRefMathSciNetGoogle Scholar
  5. [DRS06]
    Domínguez, V., Rapún, M.–L., Sayas, F.–J.: Dirac delta methods for Helmholtz transmission problems. Adv. Comput. Math. (in press).Google Scholar
  6. [KM88]
    Kleinman, R.E., Martin, P.A.: On single integral equations for the transmission problem of acoustics. SIAM J. Appl. Math., 48, 307–325 (1988).CrossRefMathSciNetGoogle Scholar
  7. [KR78]
    Kress, R., Roach, G.F.: Transmission problems for the Helmholtz equation. J. Math. Phys., 19, 1433–1437 (1978).MATHCrossRefMathSciNetGoogle Scholar
  8. [Man01]
    Mandelis, A.: Diffusion–Wave Fields. Mathematical Methods and Green Functions. Springer, New York (2001).MATHGoogle Scholar
  9. [McL00]
    McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000).MATHGoogle Scholar
  10. [RS06a]
    Rapún, M.-L., Sayas, F.-J.: Boundary integral approximation of a heat diffusion problem in time-harmonic regime. Numer. Algorithms, 41, 127–160 (2006).MATHCrossRefMathSciNetGoogle Scholar
  11. [RS06b]
    Rapún, M.-L., Sayas, F.-J.: Indirect methods with Brakhage–Werner potentials for Helmholtz transmission problems. In: Proceedings of ENUMATH 2005. Springer, New York (2006), pp. 1146–1154.Google Scholar
  12. [TSS02]
    Terrón, J.M., Salazar, A., Sánchez–Lavega, A.: General solution for the thermal wave scattering in fiber composites. J. Appl. Phys., 91, 1087–1098 (2002).CrossRefGoogle Scholar
  13. [TW93]
    Torres, R.H., Welland, G.V.: The Helmholtz equation and transmission problems with Lipschitz interfaces. Indiana Univ. Math. J., 42, 1457–1485 (1993).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • M.-L. Rapún
    • 1
  • F.-J. Sayas
    • 2
  1. 1.Universidad Politécnica de MadridSpain
  2. 2.Universidad de ZaragozaSpain

Personalised recommendations