Open Access
ARTICLE
David Stevens1, Henry Power1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 111-146, 2010, DOI:10.3970/cmes.2010.055.111
Abstract Problems involving nonlinear time-dependent heat conduction in materials which have temperature-dependent thermal properties are solved with a novel meshless numerical solution technique using multiquadric radial basis functions (RBFs). Unlike traditional RBF collocation methods, the local Hermitian interpolation (LHI) method examined here can be scaled to arbitrarily large problems without numerical ill-conditioning or computational cost issues, due to the presence of small overlapping interpolation systems which grow in number but not in size as the global dataset grows. The flexibility of the full-domain multiquadric collocation method to directly interpolate arbitrary boundary conditions is maintained, via the local interpolations.
The Kirchhoff transformation… More >
Open Access
ARTICLE
J. Trevelyan1and G. Coates1
CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 147-170, 2010, DOI:10.3970/cmes.2010.055.147
Abstract The terminology "wave boundary elements" relates to boundary elements enriched in the Partition of Unity sense by a multiple plane wave basis for the analysis of the propagation of short wavelength waves. This paper presents a variant of this approach in which the plane wave basis is selected adaptively according to an error indicator. The error indicator is residual based, and exhibits useful local and global properties. Model improvement in each adaptive iteration is carried out by the addition of new plane waves with no h-refinement. The convergence properties of the scheme are demonstrated. More >
Open Access
ARTICLE
A. Vukovic1, P. Sewell1, T. M. Benson1
CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 171-190, 2010, DOI:10.3970/cmes.2010.055.171
Abstract A fast and accurate method is developed for the analysis of a class of metal three-dimensional resonators with rotational symmetry. The analysis is formulated using the Body of Revolution approach and the Method of Analytical Regularization. This development is motivated by the need for three-dimensional analytical solvers that could enable fast and accurate analysis of photonic resonant structures which support very high Q whispering gallery modes and which are computationally challenging for numerical simulations. The paper outlines the formulation of the method and demonstrates the stability and the source of computation errors of the method. As a practical illustration, the… More >
Open Access
ARTICLE
M. A. Kelmanson1 and M. C. Tenwick1
CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 191-210, 2010, DOI:10.3970/cmes.2010.055.191
Abstract A method is presented for improving the accuracy of the widely used Gauss-Legendre Nyström method for determining approximate solutions of Fredholm integral equations of the second kind on finite intervals. The authors' recent continuous-kernel approach is generalised in order to accommodate kernels that are either singular or of limited continuous differentiability at a finite number of points within the interval of integration. This is achieved by developing a Gauss-Jacobi Nyström method that moreover includes a mean-value estimate of the truncation error of the Hermite interpolation on which the quadrature rule is based, making it particularly accurate at low orders. A… More >
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