Influence of element types on numeric error for acoustic boundary elements

Journal of Computational Acoustics

Volumn 11, Issue 3, 2003, Pages 363-386

  Marburg, Steffen ^a   Schneider, Stefan ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Boundary element method; Collocation; Discontinuous elements; Helmholtz equation; Location of collocation points; Numeric error; Superconvergence

Indexed keywords

EID: 0042450677     PISSN: 0218396X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218396X03001985     Document Type: Conference Paper

References (26)

1. K. E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, 1st edition (Cambridge University Press, 1997).
2. A. Branski, "Model of an acoustic source with discontinuous optimal elements," Archives of Acoustics, 22(4), 383 (1997).
3. A. J. Burton and G. F. Miller, "The application of integral equation methods to the numerical solution of some exterior boundary-value problems," Proc. R. Soc. Lond. 323, 201 (1971).
4. G. Chandler, Superconvergence of Numerical Solutions to Second Kind Integral Equations, Phddissertation (Australian National University, Canberra, 1979).
5. F. Chatelin and R. Lebbar, "The iterated projection solution for the Fredholm integral equation of the second kind," J. Australian Math. Soc., Series B 22, 439 (1981).
6. R. da Cunha and T. Hopkins, "The Parallel Iterative Methods (PIM) package for the solution of systems of linear equations on parallel computers," Appl. Numerical Math. 19(1-2), 33 (1995).
7. A. Elzein and R. A. Adey, "Crack analysis using discontinuous boundary elements," Proceedings of the Institution of Mechanical Engineers/Part G: Journal of Aerospace Engineering 207, 41 (1993).
8. W. F. Florez and H. Power, "Comparison between continuous and discontinuous boundary elements in the multidomain dual reciprocity method for the solution of the two-dimensional Navier-Stokes equation," Eng. Anal. Boundary Elements 25, 57 (2001).
9. W. Hackbusch, Integral Equations - Theory and Numerical Treatment, volume 120, Birkhäuser-Verlag, Basel Boston Berlin, international series of numerical mathematics edition, 1995.
10. I. Harari, K. Grosh, T. J. R. Hughes, M. Malhotra, P. M. Pinsky, J. R. Stewart, and L. L. Thompson, "Recent development in finite element methods for structural acoustics," Archives of Comput. Methods in Eng. 3(2-3), 131 (1996).
11. I. Harari and T. J. R. Hughes, "A cost comparison of boundary element and finite element methods for problems of time-harmonic acoustics," Comp. Methods in Appl. Mechanics and Eng. 97, 77 (1992).
12. F. Ihlenburg, Finite Element Analysis of Acoustic Scattering, volume 132 of Applied Mathematical Sciences (Springer Verlag, Berlin Heidelberg New York, 1998).
13. S. Marburg, "Six elements per wavelength. Is that enough?" J. Comput. Acoust. 10(1), 25 (2002).
14. S. Marburg and H.-J. Hardtke, "A study on the acoustic boundary admittance. Determination, results and consequences," Eng. Anal. Boundary Elements 23, 737 (1999).
15. S. Marburg and S. Schneider, "Performance of iterative solvers for acoustic problems. Part I: Solvers and effect of diagonal preconditioning, " Eng. Anal. Boundary Elements 27(7), 727 (2003).
16. O. I. Panič, "K voprosu o razrešimosti vnešnich kraevich zadač dlja volnovogo uravnenija i dlja sistemi uravnenij MAXWELLa," Uspechi Math. Nauk 20(1), 221 (1965).
17. J. J. d. Rego Silva, Acoustic and Elastic Wave Scattering Using Boundary Elements, volume 18 of Topics in Engineering (Computational Mechanics Publications, Southampton Boston, 1993).
18. J. J. d. Rego Silva, L. C. Wrobel, and J. C. F. Telles, "A new family of continuous/discontinuous three-dimensional boundary elements with application to acoustic wave propagation," Int. J. Num. Meth. Eng. 38, 1661 (1993).
19. Y. Saad and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM J. Scientific and Statistical Computing, 7, 856 (1986).
20. A. H. Stroud, Approximate Calculation of Multiple Integrals (Prentice-Hall, Englewood Cliffs, New Jersey, 1971).
21. A. Tadeu and J. Antonio, "Use of constant, linear and quadratic boundary elements in 3d wave diffraction analysis," Eng. Anal. Boundary Elements 24, 131 (2000).
22. J. C. F. Telles, "A self-adaptive coordinate transformation for efficient numerical evaluation of general boundary element integrals," Int. J. Numerical Methods in Eng. 24, 959 (1987).
23. L. L. Thompson and P. M. Pinsky, "Complex wave-number Fourier analysis of the p-version finite element method," Computational Mechanics 13, 255 (1994).
24. J. Trevelyan, "Use of discontinuous boundary elements for fracture mechanics analysis," Eng. Anal. Boundary Elements 10, 353 (1992).
25. T. W. Wu, A. F. Seybert, and G. C. Wan, "On the numerical implementation of a Cauchy principal value integral to insure a unique solution for acoustic radiation and scattering," J. Acoust. Soc. Am. 90, 554 (1991).
26. T. W. Wu and G. C. Wan, "Numerical modeling of acoustic radiation and scattering from thin bodies using a Cauchy principal integral equation," J. Acoust. Soc. Am. 92, 2900 (1992).