Time And Space Derivatives In A BEM
Formulation Based On The CQM With
Initial Conditions Contribution
Author(s)
A. I. Abreu, M. A. C. Ferro & W. J. Mansur
Abstract
This work is concerned with the numerical computation of time and space
derivatives of the time-domain solution of scalar wave propagation problems
using the boundary element method (TD-BEM). In the present formulation, the
BEM based on the so-called convolution quadrature method (CQM-BEM) is
employed. The CQM-BEM takes into account non-homogeneous initial
conditions by means of a general procedure, known as the initial condition
pseudo-force procedure (ICPF), which replaces the initial conditions by
equivalent pseudo-forces. The boundary integral equation with initial conditions
contribution is derived analytically and the quadrature weights of the standard
ICPF-CQM-BEM formulation are transformed in order to compute time and
space derivatives. Two numerical examples are presented at the end of the work
illustrating the efficacy of the implemented formulation.
Keywords: wave equation, time and space derivatives, boundary element
method, convolution quadrature method, initial condition pseudo-force
procedure.
1 Introduction
This work presents an application of a time-domain boundary element method
(TD-BEM) for the analysis of scalar wave propagation problems. The TD-BEM
employs the convolution quadrature method (CQM) developed by Lubich [1, 2].
In the CQM, fundamental solutions in the Laplace transformed-domain are
considered and a numerical approximation of the basic integral equations of the
Keywords
wave equation, time and space derivatives, boundary element
method, convolution quadrature method, initial condition pseudo-force
procedure.
Related Book
Other papers in this volume
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