Leevan Ling¹, Tomoya Takeuchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 99-110, 2007, DOI:10.3970/cmes.2007.020.099

Abstract We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4):1289--1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy More >

H.B. Chen¹, D.J. Fu¹, P.Q. Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 85-98, 2007, DOI:10.3970/cmes.2007.020.085

Abstract Researches today show that, both approximation and dispersion errors are encountered by classical Galerkin FEM solutions for Helmholtz equation governing the harmonic wave propagation, which leads to numerical inaccuracies especially for high wave number cases. In this paper, Local Boundary Integral Equation Method (LBIEM) is firstly implemented to solve the boundary value problem of Helmholtz equation. Then the regularized LBIE is proposed to overcome the singularities of the boundary integrals in the LBIEM. Owing to the advantages of the Moving Least Square Approximation (MLSA), the frequency-dependent basis functions modified by the harmonic wave propagation solutions More >

Alfredo Nicolás¹, Blanca Bermúdez²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 73-84, 2007, DOI:10.3970/cmes.2007.020.073

Abstract 2D viscous incompressible flows are presented from the unsteady Navier-Stokes equations in its velocity-vorticity formulation. The results are obtained using a simple numerical procedure based on a fixed point iterative process to solve the nonlinear elliptic system that results once a second order time discretization is performed. Flows on the un-regularized unit driven cavity problem are reported up to Reynolds numbers Re=4000 to compare them with those reported by other authors, mainly solving the steady problem, and supposed to be correct. Moreover, results are reported for Re = 1000, 4000, 5000, and 10000 to see how More >

A. Arockiarajan¹, A. Menzel²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 55-72, 2007, DOI:10.3970/cmes.2007.020.055

Abstract To study rate-dependent properties of piezoelectric materials a micro-mechanically motivated model is applied in this work. The developed framework is embedded into a coupled three-dimensional finite element setting, whereby each element is assumed to represent one grain and, moreover, possesses a random initialisation of the underlying polarisation direction. Furthermore, an energy-based criterion is used for the initiation of the onset of domain switching and the subsequent propagation of domain wall motion during the switching process is modelled via a linear kinetics theory. The interaction between individual grains is thereby incorporated by means of a probabilistic More >

N. Osawa¹, K. Hashimoto¹, J. Sawamura¹, J. Kikuchi², Y. Deguchi², T. Yamaura²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 43-54, 2007, DOI:10.3970/cmes.2007.020.043

Abstract A new hypothesis regarding heat transmission during line heating is proposed. It states that the distribution of the temperature of the gas adjacent to the plate, T_G, and the overall local heat transfer coefficient, α, depend only on the distance from the torch. An identification technique for T_G and α is developed. The validity of the employed hypothesis and the proposed technique is demonstrated by comparing the measured and identified T_G during a spot heating test. The plate temperature calculated by direct heat conduction analysis closely approximates the one measured for the spot and line heating tests, More >

Chany Lee¹, Chang-Hwan Im², Hyun-Kyo Jung³, Hong-Kyu Kim⁴, Do Wan Kim⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 35-42, 2007, DOI:10.3970/cmes.2007.020.035

Abstract In the present study, a residual-based a posteriori error estimation for a kind of meshless method, called fast moving least square reproducing kernel (FMLSRK) method is proposed. The proposed error estimation technique does not require any integration cells in evaluating error norm but recovers the exact solutions in a virtual area defined by a dilation parameter of FMLSRK and node density. The proposed technique was tested on typical electrostatic problems with gird or random node sets and the simulation results show that the proposed error estimation technique can be applied to adaptive node refinement process More >

Berardi Sensale Cozzano¹, Berardi Sensale Rodríguez²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 21-34, 2007, DOI:10.3970/cmes.2007.020.021

Abstract In this paper, the Trefftz method is applied to solve linear viscoelasticity problems in the time domain, using Trefftz elastic series and considering the viscoelastic components in each time domain as fictitious body forces. The direct application of the Trefftz method to elastic problems is typically constrained to those cases in which the Navier equation is homogeneous. In the presence of body forces, the method of the particular solution or the method of the generalized particular solution should be used, depending on whether the body forces are constant or not inside the considered domain. Many More >

L. Wang¹, S. Zhang, W. M. Gao, X. Wang

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 11-20, 2007, DOI:10.3970/cmes.2007.020.011

Abstract In this paper, the penetration of a knife through a plain woven fabric is simulated with the finite element method to understand the process of stabbing and the mechanism of fiber breakage. The model focuses on the study of the deformation of individual yarns, and the effects of their material properties and fabric structure on the stabbing resistant force. The performance of the fabric is analyzed as a response of stabbing and the stress distributions in yarn transverse and longitudinal directions. An equation derived from energy and momentum conservations of the knife is proposed to More >

J. M. F. Trindade¹, J. C. F. Pereira²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 1-10, 2007, DOI:10.3970/cmes.2007.020.001

Abstract In this paper, we discuss the efficiency and speed-up of parallel-in-time calculations of the unsteady incompressible Navier-Stokes equations in a PC-cluster. The parallel-in-time method is based on the alternate use of coarse global sequential solvers with fine local parallel ones in an iterative predictor-corrector fashion. Therefore, the efficiency of parallel calculations is strongly dependent on the number of iterations required for convergence. The one-dimensional scalar transport equation and the two-dimensional incompressible unsteady form of the Navier-Stokes equations were used to conduct numerical experiments to derive some conclusions concerning the accuracy and convergence of the iterative… More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², P. Solek³, L. Starek³

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 247-262, 2007, DOI:10.3970/cmes.2007.019.247

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-D) and three-dimensional (3-D) axisymmetric piezoelectric solids with continuously varying material properties. Axial symmetry of geometry and boundary conditions reduces the original 3-d boundary value problem into a 2-d problem. Stationary problems are considered in this paper. The axial cross section is discretized into small circular subdomains surrounding nodes randomly spread over the analyzed domain. A unit step function is used as the test functions in the local weak-form. Then, the derived local integral equations (LBIEs) involve only contour-integrals More >