Open Access

ARTICLE

An Adaptive Fast Multipole Approach to 2D Wave Propagation

V. Mallardo¹, M.H. Aliabadi²

1 Corresponding author. mlv@unife.it. Dep. Architecture, University of Ferrara, Via Quartieri 844121 Ferrara, Italy
2 m.h.aliabadi@imperial.ac.uk. Dep. Aeronautics, Imperial College London, South Kensington Campus, UK

Computer Modeling in Engineering & Sciences 2012, 87(2), 77-96. https://doi.org/10.3970/cmes.2012.087.077

Abstract

The present paper intends to couple the Fast Multipole Method (FMM) with the Boundary Element Method (BEM) in the 2D scalar wave propagation. The procedure is aimed at speeding the computation of the integrals involved in the governing Boundary Integral Equations (BIEs) on the basis of the distance between source point and integration element. There are three main contributions. First, the approach is of adaptive type in order to reduce the number of floating-point operations. Second, most integrals are evaluated analytically: the diagonal and off-diagonal terms of the H and G matrices by consolidated techniques, whereas the moment Mk by a procedure developed by the authors. Third, the article is enriched by Fortran 90 schemes that, specifically developed by the authors, allow the optimum construction of the quad-tree and of the iterative system of equations. The Generalized Minimal Residual Solver is adopted to improve the overall computational efficiency. Some numerical examples are shown to demonstrate the reliability of the method.

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Keywords

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