CMES-Vol. 58, No. 3, 2010

Open Access

ARTICLE

A Spectral Boundary Element Method for Scattering Problems
J. Tausch¹, J. Xiao²
CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 221-246, 2010, DOI:10.3970/cmes.2010.058.221
Abstract A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is discretized by a Nyström method and is evaluated efficiently using a sequence of FFTs. The potential due to the local part is approximated by a truncated series in the mollification parameter. The smooth approximation of the kernel is obtained by multiplication of its Fourier transform with a filter. We will show that for a rational More >

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Analysis of a Crack in a Thin Adhesive Layer between Orthotropic Materials: An Application to Composite Interlaminar Fracture Toughness Test
L. Távara¹, V. Manticˇ ¹, E. Graciani¹, J. Cañas¹, F. París¹
CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 247-270, 2010, DOI:10.3970/cmes.2010.058.247
Abstract The problem of a crack in a thin adhesive layer is considered. The adherents may have orthotropic elastic behavior which allows composite laminates to be modeled. In the present work a linear elastic-brittle constitutive law of the thin adhesive layer, called weak interface model, is adopted, allowing an easy modeling of crack propagation along it. In this law, the normal and tangential stresses across the undamaged interface are proportional to the relative normal and tangential displacements, respectively. Interface crack propagation is modeled by successive breaking of the springs used to discretize the weak interface. An… More >

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On the application of the Fast Multipole Method to Helmholtz-like problems with complex wavenumber
A. Frangi¹, M. Bonnet²
CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 271-296, 2010, DOI:10.3970/cmes.2010.058.271
Abstract This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form k = (α + iβ)ϑ, with α = 0,±1 and β > 0, which, the paucity of available studies notwithstanding, arise for a wealth of different physical problems. It is suggested that a simple point-wise error indicator can provide an a-priori indication on the number N of terms to be employed in the Gegenbauer addition formula in order to achieve a prescribed accuracy when integrating single layer potentials over surfaces. For β ≥ 1 it More >

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Galerkin Boundary Integral Analysis forthe 3D Helmholtz Equation
M. R. Swager¹, L. J. Gray², S. Nintcheu Fata²
CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 297-312, 2010, DOI:10.3970/cmes.2010.058.297
Abstract A linear element Galerkin boundary integral analysis for the three-dimensional Helmholtz equation is presented. The emphasis is on solving acoustic scattering by an open (crack) surface, and to this end both a dual equation formulation and a symmetric hypersingular formulation have been developed. All singular integrals are defined and evaluated via a boundary limit process, facilitating the evaluation of the (finite) hypersingular Galerkin integral. This limit process is also the basis for the algorithm for post-processing of the surface gradient. The analytic integrations required by the limit process are carried out by employing a Taylor More >

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