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Numerical Computation of Space Derivatives by the Complex-Variable-Differentiation Method in the Convolution Quadrature Method Based BEM Formulation

A.I. Abreu1, W.J. Mansur1, D. Soares Jr1,2, J.A.M. Carrer3
Department of Civil Engineering, COPPE/Federal University of Rio de Janeiro, CP 68506, CEP 21945-970, Rio de Janeiro, RJ, Brazil. Email: anai@coc.ufrj.br, webe@coc.ufrj.br
Structural Engineering Department, Federal University of Juiz de Fora, Cidade Universitária, CEP 36036-330, Juizde Fora, MG, Brazil. E-mail: delfim.soares@ufjf.edu.br
PPGMNE: Programa de Pós-Graduação em Métodos Numéricos em Engenharia, Universidade Federal do Paraná, CP 19011, CEP 81531-990, Curitiba, PR, Brasil. E-mail: carrer@mat.ufpr.br

Computer Modeling in Engineering & Sciences 2008, 30(3), 123-132. https://doi.org/10.3970/cmes.2008.030.123

Abstract

This paper is concerned with the numerical computation of space derivatives of a time-domain (TD-) Boundary Element Method (BEM) formulation for the analysis of scalar wave propagation problems. In the present formulation, the Convolution Quadrature Method (CQM) is adopted, i.e., the basic integral equation of the TD-BEM is numerically substituted by a quadrature formula, whose weights are computed using the Laplace transform of the fundamental solution and a linear multi-step method. In order to numerically compute space derivatives, the present work properly transforms the quadrature weights of the CQM-BEM, adopting the so-called Complex-Variable-Differentiation Method (CVDM). Numerical examples are presented at the end of the paper illustrating the accuracy and potentialities of the proposed formulation.

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Abreu, A., Mansur, W., Jr, D. S., Carrer, J. (2008). Numerical Computation of Space Derivatives by the Complex-Variable-Differentiation Method in the Convolution Quadrature Method Based BEM Formulation. CMES-Computer Modeling in Engineering & Sciences, 30(3), 123–132.



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