C.-S. Liu¹, C.-W. Chang², J.-R. Chang²

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 67-82, 2006, DOI:10.3970/cmes.2006.012.067

Abstract In this paper we are concerned with the backward problems governed by differential equations. It is a first time that we can construct a backward time dynamics on the past cone, such that an augmented dynamical system of the Lie type X^˙ = B(X,t)X with t ∈ R⁻, X ∈ Mⁿ⁺¹ lying on the past cone and B ∈ so(n,1), was derived for the backward differential equations system x^· =f(x,t), t ∈ R⁻, x ∈ Rⁿ. These two differential equations systems are mathematically equivalent. Then we apply the backward group preserving scheme (BGPS), which is an explicit single-step algorithm… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 55-66, 2006, DOI:10.3970/cmes.2006.012.055

Abstract In this paper we are concerned with the numerical integration of Burgers equation backward in time. We construct a one-step backward group preserving scheme (BGPS) for the semi-discretization of Burgers equation. The one-step BGPS is very effectively to calculate the solution at an initial time t = 0 from a given final data at t = T, which with a time stepsize equal to T and with a suitable grid length produces a highly accurate solution never seen before. Under noisy final data the BGPS is also robust to against the disturbance. When the solution appears steep gradient, More >

S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 27-40, 2006, DOI:10.3970/cmes.2006.012.027

Abstract In this paper a new boundary method for eigenproblems with the Helmholtz equation in simply and multiply connected domains is presented. The solution of an eigenvalue problem is reduced to a sequence of inhomogeneous problems with the differential operator studied. The method shows a high precision in simply and multiply connected domains and does not generate spurious eigenvalues. The results of the numerical experiments justifying the method are presented. More >

A.Kurenkov¹, A.Thess², H.Babovsky³

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.1, pp. 47-58, 2006, DOI:10.3970/fdmp.2006.002.047

Abstract A possibility for the determination of the interface between two electrically conducting fluids in cylindrical geometry is presented. The fluids with different conductivities are situated in an infinite cylinder. Along the axis of the cylinder a homogeneous electrical current is applied. The perturbation of the interface leads to an inhomogeneous electrical current and, therefore, results in an electrical potential change in the fluids and a magnetic field modification outside the fluids. The dependence of the electrical potential on the interface shape is obtained analytically. The interface profile is then recovered from data of the electrical More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², F. Garcia-Sanche³, M. Wünsche²

CMC-Computers, Materials & Continua, Vol.4, No.2, pp. 109-118, 2006, DOI:10.3970/cmc.2006.004.109

Abstract Piezoelectric materials have wide range engineering applications in smart structures and devices. They have usually anisotropic properties. Except this complication electric and mechanical fields are coupled each other and the governing equations are much more complex than that in the classical elasticity. Thus, efficient computational methods to solve the boundary or the initial-boundary value problems for piezoelectric solids are required. In this paper, the Meshless local Petrov-Galerkin (MLPG) method with a Heaviside step function as the test functions is applied to solve two-dimensional (2-D) piezoelectric problems. The mechanical fields are described by the equations of… More >

G.S. Palani¹, Nagesh R. Iyer¹, B. Dattaguru²

Structural Durability & Health Monitoring, Vol.1, No.2, pp. 107-120, 2005, DOI:10.3970/sdhm.2005.001.107

Abstract A posteriori error estimation and adaptive refinement technique for 2-D/3-D crack problems is the state-of-the-art. In this paper a new a posteriori error estimator based on strain energy release rate (SERR) or stress intensity factor (SIF) at the crack tip region has been proposed and used along with the stress based error estimator for reliable fracture analysis of 2-D crack problems. The proposed a posteriori error estimator is called the K-S error estimator. Further, h-adaptive mesh refinement strategy which can be used with K-S error estimator has been proposed for fracture analysis of 2-D crack problems. The performance More >

J. Sladek¹, V. Sladek¹, J. Krivacek¹, Ch. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.3, pp. 259-270, 2005, DOI:10.3970/cmes.2005.008.259

Abstract A meshless method based on the local Petrov-Galerkin approach is presented for stress analysis in three-dimensional (3-d) axisymmetric linear elastic solids with continuously varying material properties. The inertial effects are considered in dynamic problems. A unit step function is used as the test functions in the local weak-form. It is leading to local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace-transform technique is applied and the LBIEs are given in the Laplace-transformed domain. Axial symmetry of the geometry and the boundary conditions for a 3-d linear elastic solid reduces the original 3-d boundary More >

D.L. Young^1,2, J.W. Ruan²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 223-232, 2005, DOI:10.3970/cmes.2005.007.223

Abstract The applications of the method of fundamental solutions (MFS) for modeling the scattering of time-harmonic electromagnetic fields, which are governed by vector Helmholtz equations with coupled boundary conditions, are described. Various perfectly electric conductors are considered as the scatterers to investigate the accuracy of the numerical performance of the proposed procedure by comparing with the available analytical solutions. It is also the intention of this study to reveal the characteristics of the algorithms by comparisons with other numerical methods. The model is first validated to the exact solutions of the electromagnetic wave propagation problems for More >

L. Mai-Cao¹, T. Tran-Cong²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 149-172, 2005, DOI:10.3970/cmes.2005.007.149

Abstract The Indirect Radial Basis Function Network (IRBFN) method has been reported to be a highly accurate tool for approximating multivariate functions and solving elliptic partial differential equations (PDEs). The present method is a truly meshless method as defined in [\citet *{Atluri_Shen_02a}]. A recent development of the method for solving transient problems is presented in this paper. Two numerical schemes combining the IRBFN method with different time integration techniques based on either fully or semi-discrete framework are proposed. The two schemes are implemented making use of Hardy's multiquadrics (MQ) and Duchon's thin plate splines (TPS). Some More >

Y.C. Hon¹, T. Wei²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 119-132, 2005, DOI:10.3970/cmes.2005.007.119

Abstract We propose in this paper an effective meshless and integration-free method for the numerical solution of multidimensional inverse heat conduction problems. Due to the use of fundamental solutions as basis functions, the method leads to a global approximation scheme in both the spatial and time domains. To tackle the ill-conditioning problem of the resultant linear system of equations, we apply the Tikhonov regularization method based on the generalized cross-validation criterion for choosing the regularization parameter to obtain a stable approximation to the solution. The effectiveness of the algorithm is illustrated by several numerical two- and More >