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Scalar wave equation by the boundary element method: a D-BEM approach with non-homogeneous initial conditions

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Abstract

This work is concerned with the development of a D-BEM approach to the solution of 2D scalar wave propagation problems. The time-marching process can be accomplished with the use of the Houbolt method, as usual, or with the use of the Newmark method. Special attention was devoted to the development of a procedure that allows for the computation of the initial conditions contributions. In order to verify the applicability of the Newmark method and also the correctness of the expressions concerned with the computation of the initial conditions contributions, four examples are presented and the D-BEM results are compared with the corresponding analytical solutions.

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References

  1. Beskos DE (1997) Boundary elements in dynamic analysis: part II (1986–1996). Appl Mech Rev 50: 149–197

    Article  Google Scholar 

  2. Beskos DE (2003) Dynamic analysis of structures and structural systems. In: Beskos DE, Maier G (eds) Boundary element advances in solid mechanics. CISM, Udine

    Google Scholar 

  3. Mansur WJ (1983) A Time-stepping technique to solve wave propagation problems using the boundary element method. Ph.D. Thesis, University of Southampton

  4. Dominguez J (1993) Boundary elements in dynamics. Computational Mechanics Publications, Southampton, Boston

    MATH  Google Scholar 

  5. Carrer JAM, Mansur WJ (2002) Time-dependent fundamental solution generated by a not impulsive source in the boundary element method analysis of the 2D scalar wave equation. Commun Numer Methods Eng 18: 277–285

    Article  MATH  Google Scholar 

  6. Demirel V, Wang S (1987) Efficient boundary element method for two-dimensional transient wave propagation problems. Appl Math Model 11: 411–416

    Article  MATH  MathSciNet  Google Scholar 

  7. Mansur WJ, deLima-Silva W (1992) Efficient time truncation in two-dimensional BEM analysis of transient wave propagation problems. Earthquake Eng Struct Dyn 21: 51–63

    Article  Google Scholar 

  8. Soares D Jr, Mansur WJ (2004) Compression of time generated matrices in two-dimensional time-domain elastodynamic BEM analysis. Int J Numer Methods Eng 61: 1209–1218

    Article  MATH  Google Scholar 

  9. Carrer JAM, Mansur WJ (2006) Solution of the two-dimensional scalar wave equation by the time-domain boundary element method: lagrange truncation strategy in time integration. Struct Eng Mech 23: 263–278

    Google Scholar 

  10. Carrer JAM, Mansur WJ (2004) Alternative time-marching schemes for elastodynamic analysis with the domain boundary element method formulation. Comput Mech 34: 387–399

    Article  MATH  Google Scholar 

  11. Hatzigeorgiou GD, Beskos DE (2002) Dynamic elastoplastic analysis of 3D structures by the domain/boundary element method. Comput Struct 80: 339–347

    Article  Google Scholar 

  12. Kontoni DPN, Beskos DE (1993) Transient dynamic elastoplastic analysis by the dual reciprocity BEM. Eng Anal Bound Elements 12: 1–16

    Article  Google Scholar 

  13. Partridge PW, Brebbia CA, Wrobel LC (1992) The dual reciprocity boundary element method. Computational Mechanics Publications, Southampton, Boston

    MATH  Google Scholar 

  14. Agnantiaris JP, Polyzos D, Beskos DE (1996) Some studies on dual reciprocity BEM for elastodynamic analysis. Comput Mech 17: 270–277

    Article  Google Scholar 

  15. Agnantiaris JP, Polyzos D, Beskos DE (1998) Three-dimensional structural vibration analysis by the dual reciprocity BEM. Comput Mech 21: 372–381

    Article  MATH  Google Scholar 

  16. Houbolt JC (1950) A recurrence matrix solution for the dynamic response of elastic aircraft. J Aeronaut Sci 17: 540–550

    MathSciNet  Google Scholar 

  17. Souza LA, Carrer JAM, Martins CJ (2004) A fourth order finite difference method applied to elastodynamics: finite element and boundary element formulations. Struct Eng Mech 17: 735–749

    Google Scholar 

  18. Chien CC, Chen YH, Chuang CC (2003) Dual reciprocity BEM analysis of 2D transient elastodynamic problems by time-discontinuous galerkin FEM. Eng Anal Bound Elements 27: 611–624

    Article  MATH  Google Scholar 

  19. Bathe KJ (1996) Finite element procedures. Prentice Hall Inc., New Jersey

    Google Scholar 

  20. Cook RD, Malkus DS, Plesha ME (1989) Concepts and applications of finite element analysis. Wiley, New York

    MATH  Google Scholar 

  21. Newmark NM (1959) A method of computation for structural dynamics. ASCE J Eng Mech Div 85: 67–94

    Google Scholar 

  22. Carrer JAM, Mansur WJ (1996) Time-Domain BEM analysis for the 2D scalar wave equation: initial conditions contributions to space and time derivatives. Int J Numer Methods Eng 39: 2169–2188

    Article  MATH  Google Scholar 

  23. Stephenson G (1970) An introduction to partial differential equations for science students. Longman, London

    Google Scholar 

  24. Kreyszig E (1999) Advanced engineering mathematics, 8th edn. Wiley, New York

    Google Scholar 

  25. Abreu AI, Mansur WJ, Carrer JAM (2006) Initial conditions contributions in a BEM formulation based on the convolution quadrature method. Int J Numer Methods Eng 67: 417–434

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. PPGMNE: Programa de Pós-Graduação em Métodos Numéricos em Engenharia, Universidade Federal do Paraná, Caixa Postal 19011, Curitiba, PR, CEP 81531-990, Brazil

    J. A. M. Carrer & R. J. Vanzuit

  2. Programa de Engenharia Civil, COPPE/UFRJ, Universidade Federal do Rio de Janeiro, Caixa Postal 68506, Rio de Janeiro, CEP 21945-970, Brazil

    W. J. Mansur

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  1. J. A. M. Carrer
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  2. W. J. Mansur
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  3. R. J. Vanzuit
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Correspondence to J. A. M. Carrer.

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Carrer, J.A.M., Mansur, W.J. & Vanzuit, R.J. Scalar wave equation by the boundary element method: a D-BEM approach with non-homogeneous initial conditions. Comput Mech 44, 31–44 (2009). https://doi.org/10.1007/s00466-008-0353-4

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  • DOI: https://doi.org/10.1007/s00466-008-0353-4

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