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
CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 123-132, 2008, DOI: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… More >
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