Abstract
This work presents a boundary element method formulation for the analysis of scalar wave propagation problems. The formulation presented here employs the so-called operational quadrature method, by means of which the convolution integral, presented in time-domain BEM formulations, is substituted by a quadrature formula, whose weights are computed by using the Laplace transform of the fundamental solution and a linear multistep method. Two examples are presented at the end of the article with the aim of validating the formulation.
Highlights
Due to the importance and wide range of application of the analyses concerning scalar wave propagation and elastodynamics, several BEM formulations were developed during the last years and, for the purposes of the present work, they will be classified in time-domain and transformed-domain formulations
The BEM formulation developed in this work for the solution of problems governed by the scalar wave equation employs the fundamental solution in the Laplace domain and provides direct solution to the problem in the timedomain
The formulation developed in this work, based on the operational quadrature method (OQM), shows an elegant way of solving the wave propagation problem, provided one has the corresponding fundamental solution in the Laplace domain
Summary
Due to the importance and wide range of application of the analyses concerning scalar wave propagation and elastodynamics, several BEM formulations were developed during the last years and, for the purposes of the present work, they will be classified in time-domain and transformed-domain formulations. The BEM formulation developed in this work for the solution of problems governed by the scalar wave equation employs the fundamental solution in the Laplace domain and provides direct solution to the problem in the timedomain. This characteristic of the formulation turns it very attractive. With the aim of validating the extension of the formulation to the BEM and of verifying the accuracy of the results that it can produce
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