Premium
Initial conditions contribution in a BEM formulation based on the convolution quadrature method
Author(s) -
Abreu A. I.,
Mansur W. J.,
Carrer J. A. M.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1645
Subject(s) - laplace transform , quadrature (astronomy) , boundary element method , scalar (mathematics) , convolution (computer science) , mathematics , nyström method , mathematical analysis , numerical integration , boundary value problem , laplace's equation , finite element method , computer science , geometry , physics , electronic engineering , engineering , machine learning , artificial neural network , thermodynamics
This work presents a two‐dimensional boundary element method (BEM) formulation for the analysis of scalar wave propagation problems. The formulation is based on the so‐called convolution quadrature method (CQM) by means of which the convolution integral, presented in time‐domain BEM formulations, is numerically substituted by a quadrature formula, whose weights are computed using the Laplace transform of the fundamental solution and a linear multistep method. This BEM formulation was initially developed for scalar wave propagation problems with null initial conditions. In order to overcome this limitation, this work presents a general procedure that enables one to take into account non‐homogeneous initial conditions, after replacing the initial conditions by equivalent pseudo‐forces. The numerical results included in this work show the accuracy of the proposed BEM formulation and its applicability to such kind of analysis. Copyright © 2006 John Wiley & Sons, Ltd.