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Fast Galerkin BEM for 3D-potential theory

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Abstract

This paper is concerned with the development of a fast spectral method for solving direct and indirect boundary integral equations in 3D-potential theory. Based on a Galerkin approximation and the Fast Fourier Transform, the proposed method is a generalization of the precorrected-FFT technique to handle not only single-layer potentials but also double-layer potentials and higher-order basis functions. Numerical examples utilizing piecewise linear shape functions are presented to illustrate the performance of the method.

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References

  1. Banerjee PK (1994). The boundary element methods in engineering. McGraw-Hill, London

    Google Scholar 

  2. Bespalov AN (2000). On the use of a regular grid for implementation of boundary integral methods for wave problems. Russ J Numer Anal Math Model 15(6): 469–488

    Article  MathSciNet  MATH  Google Scholar 

  3. Bonnet M (1995). Boundary integral equation methods for solids and fluids. Wiley, New York

    Google Scholar 

  4. Brandt A (1991). Multilevel computations of integral transforms and particle interactions with oscillatory kernels. Comput Phys Commun 65: 24–38

    Article  MathSciNet  MATH  Google Scholar 

  5. Dunavant DA (1985). High degree efficient symmetrical Gaussian quadrature rules for the triangle. Int J Numer Methods Eng 21: 129–1148

    Article  MathSciNet  MATH  Google Scholar 

  6. Gray LJ, Glaeser JM and Kaplan T (2004). Direct evaluation of hypersingular Galerkin surface integrals. SIAM J Sci Comput 25(5): 1534–1556

    Article  MathSciNet  MATH  Google Scholar 

  7. Greengard L and Rokhlin V (1987). A fast algorithm for particle simulations. J Comput Phys 73: 325–348

    Article  MathSciNet  MATH  Google Scholar 

  8. Hu H, Blaauw DT, Zolotov V, Gala K, Zhao M, Panda R and Sapatnekar S (2003). Fast on-chip inductance simulation using a precorrected-FFT method. IEEE Trans Comput Aided Des Integr Circuits Syst 22(1): 49–66

    Article  Google Scholar 

  9. Lage C and Schwab C (1998). Wavelet Galerkin algorithms for boundary integral equations. SIAM J Sci Stat Comput 20: 2195– 2222

    Article  MathSciNet  Google Scholar 

  10. Lutz AD and Gray LJ (1993). Exact evaluation of singular boundary integrals without CPV. Comm Num Meth Eng 9: 909–915

    Article  MATH  Google Scholar 

  11. Masters N and Ye W (2004). Fast BEM solution for coupled 3D electrostatic and linear elastic problems. Eng Anal Bound Elem 28: 1175–1186

    Article  MATH  Google Scholar 

  12. Nie X-C, Li L-W and Yuan N (2002). Precorrected-FFT algorithm for solving combined field integral equations in electromagnetic scattering. J Electromagn Waves Appl 16(8): 1171–1187

    Article  Google Scholar 

  13. Nishimura N (2002). Fast multipole accelerate boundary integral equation methods. ASME Appl Mech Rev 55(4): 299–324

    Article  Google Scholar 

  14. París F and Canãs J (1997). Boundary element method: fundamentals and applications. Oxford University Press, New York

    MATH  Google Scholar 

  15. Phillips JR and White JK (1997). A precorrected-FFT method for electrostatic analysis of complicated 3-D structures. IEEE Trans Comput Aided Des Integr Circuits Syst 16(10): 1059–1072

    Article  Google Scholar 

  16. Pierce AP and Napier JAL (1995). A spectral multipole method for efficient solution of large-scale boundary element models in elastostatics. Int J Numer Meth eng 38(23): 4009–4034

    Article  Google Scholar 

  17. Press WH, Teukolsky SA, Vertterling WT and Flannery BP (1986). Numerical recipes: the art of scientific computing. Cambridge University Press, Cambridge

    Google Scholar 

  18. Richardson JD, Gray LJ, Kaplan T and Napier JAL (2001). Regularized spectral multipole BEM for plane elasticity. Eng Anal Bound Elem 25: 297–311

    Article  MATH  Google Scholar 

  19. Saad Y (1993). A flexible inner-outer preconditioned GMRES algorithm. SIAM J Sci Comput 14(2): 461–469

    Article  MathSciNet  MATH  Google Scholar 

  20. Saad Y (2003). Iterative methods for sparse linear systems. SIAM, Philadelphia

    MATH  Google Scholar 

  21. Sleijpen GLG and Fokkema DR (1993). BiCGSTAB(l) for linear equations involving unsymmetric matrices with complex spectrum. ETNA 1: 11–32

    MathSciNet  MATH  Google Scholar 

  22. Tausch J (2003). Sparse BEM for potential theory and Stokes flow using variable order wavelets. Comput Mech 32(4–6): 312–318

    Article  MathSciNet  MATH  Google Scholar 

  23. Tissari S and Rahola J (2003). A precorrected-FFT method to accelerate the solution of the forward problem in magnetoencephalography. Phys Med Biol 48: 523–541

    Article  Google Scholar 

  24. Van der Vorst HA and Vuik C (1994). GMRESR: a family of nested GMRES methods. Num Lin Alg Appl 14: 369–386

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Computer Science and Mathematics Division, Oak Ridge National Laboratory, P.O. Box 2008, MS 6367, Oak Ridge, TN, 37831-6367, USA

    Sylvain Nintcheu Fata

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  1. Sylvain Nintcheu Fata
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Correspondence to Sylvain Nintcheu Fata.

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Fata, S.N. Fast Galerkin BEM for 3D-potential theory. Comput Mech 42, 417–429 (2008). https://doi.org/10.1007/s00466-008-0251-9

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  • DOI: https://doi.org/10.1007/s00466-008-0251-9

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