CMES-Vol. 84, No. 1, 2012

Open Access

ARTICLE

On the Determination of the Singular Sturm-Liouville Operator from Two Spectra
Etibar S. Panakhov¹, Murat Sat²
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 1-12, 2012, DOI:10.3970/cmes.2012.084.001
Abstract In this paper an inverse problem by two given spectrum for a second-order differential operator with coulomb singularity of the type A/x in zero point ( here A is constant), is studied. It is well known that two spectrum {λ_n} and {µ_n} uniquely determine the potential function q(x) in the singular Sturm-Liouville equation defined on interval (0,π]. The aim of this paper is to prove the generalized degeneracy of the kernel K(x,t) . In particular, we obtain a new proof of the Hochstadt's theorem concerning the structure of the difference q^~(x) - q(x). More >

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ARTICLE

Implementation of a Parallel Dual Reciprocity Boundary Element Method for the Solution of Coupled Thermoelasticity and Thermoviscoelasticity Problems
M. Koyuncu¹, F. Y. Ikikat¹, G. C. Icoz², B. Baranoglu³, A. Yazici²
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 13-26, 2012, DOI:10.3970/cmes.2012.084.013
Abstract A parallel dual reciprocity boundary element method solution to thermoelasticity and thermoviscoelasticity problems is proposed. The DR-BEM formulation is given in Fourier Transform Space where the Time Space solutions are obtained through inverse Fourier Transform. The parallellization of the code is achieved through solving each frequency at a distinct computational node. The implemented parallel code is tested on 64-core IBM blade servers and it is seen that a linear speed-up is achieved. More >

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An Operator Splitting Approximation Combined With The SUPG Method For Transport Equations With Nonlinear Reaction Term
O. Baysal¹, G. Tanoglu²
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 27-40, 2012, DOI:10.3970/cmes.2012.084.027
Abstract In this work, an operator splitting method is proposed in order to obtain a stable numerical solution for transport equation with non-linear reaction term. We split the transport equation into a reaction part and an advection diffusion part. The former one which becomes a nonlinear ordinary differential equation can be approximated by the simple higher order integrator or solved exactly. The later one is approximated by the Streamline-Upwind Petrov-Galerkin (SUPG) method combined with the generalized Euler time integration (θ-method). Numerical results that illustrate the good performance of this method are reported. More >

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High-Performance 3D Hybrid/Mixed, and Simple 3D Voronoi Cell Finite Elements, for Macro- & Micro-mechanical Modeling of Solids, Without Using Multi-field Variational Principles
P. L. Bishay¹, S.N. Atluri¹
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 41-98, 2012, DOI:10.3970/cmes.2012.084.041
Abstract Higher-order two-dimensional as well as low and higher-order three-dimensional new Hybrid/Mixed (H/M) finite elements based on independently assumed displacement, and judiciously chosen strain fields, denoted by HMFEM-2, are developed here for applications in macro-mechanics. The idea of these new H/M finite elements is based on collocating the components of the independent strain field, with those derived from the independently assumed displacement fields at judiciously and cleverly chosen collocation points inside the element. This is unlike the other techniques used in older H/M finite elements where a two-field variational principle was used in order to enforce both equilibrium and compatibility conditions… More >

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