Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 179-196, 2006, DOI:10.3970/cmes.2006.015.179

Abstract This paper studies the numerical computations of the second-order singularly perturbed boundary value problems (SPBVPs). In order to depress the singularity we consider a coordinate transformation from the x-domain to the t-domain. The relation between singularity and stiffness is demonstrated, of which the coordinate transformation parameter λ plays a key role to balance these two tendencies. Then we construct a very effective Lie-group shooting method to search the missing initial condition through a weighting factor r ∈ (0,1) in the t-domain formulation. For stabilizing the new method we also introduce two new systems by a translation of More >

B. Yang², V. K. Tewary³

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 165-178, 2006, DOI:10.3970/cmes.2006.015.165

Abstract Green's function (GF) modeling of defects may take effect only if the GF as well as its various integrals over a line, a surface and/or a volume can be efficiently evaluated. The GF is needed in modeling a point defect, while integrals are needed in modeling line, surface and volumetric defects. In a matrix of multilayered, generally anisotropic and linearly elastic and piezoelectric materials, the GF has been derived by applying 2D Fourier transforms and the Stroh formalism. Its use involves another two dimensions of integration in the Fourier inverse transform. A semi-analytical scheme has… More >

A. Wacher¹, D. Givoli²

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 147-164, 2006, DOI:10.3970/cmes.2006.015.147

Abstract The recently proposed String Gradient Weighted Moving Finite Element (SGWMFE) method is extended to include remeshing and refining. The method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to the nonlinear time-dependent two-dimensional shallow water equations, under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation. Such effects are of major importance in geophysical fluid dynamics applications. Two deficiencies of the original SGWMFE method are (1) possible tangling of the mesh… More >

S. Chantasiriwan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 137-146, 2006, DOI:10.3970/cmes.2006.015.137

Abstract The multiquadric collocation method is the collocation method based on radial basis function known as multiquadrics. It has been successfully used to solve several linear and nonlinear problems. Although fluid flow problems are among problems previously solved by this method, there is still an outstanding issue regarding the influence of the free parameter of multiquadrics (or the shape parameter) on the performance of the method. This paper provides additional results of using the multiquadric collocation method to solve the lid-driven cavity flow problem. The method is used to solve the problem in the stream function-vorticity More >

Sarang Seyrafian¹, Behrouz Gatmiri², Asadollah Noorzad³

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 115-126, 2006, DOI:10.3970/cmes.2006.015.115

Abstract An analytical solution is presented for the response of a non-homogeneous saturated poroelastic half-space under the action of a time-harmonic vertical point load on its surface. The shear modulus is assumed to increase continuously with depth and also the media is considered to obey Biot's poroelastic theory. The system of governing partial differential equations, based on the mentioned assumptions, is converted to ordinary differential equations' system by means of Hankel integral transforms. Then the system of equations is solved by use of generalized power series(Frobenius method) and the expressions for displacements in the interior of More >

N.S.Mera¹, L. Elliott², D.B.Ingham²

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 107-114, 2006, DOI:10.3970/cmes.2006.015.107

Abstract The purpose of this study is to investigate the efficiency, accuracy and rate of convergence of an evolutionary algorithm for detecting inclusions parametrised by superellipses in non-destructive evaluation and testing. The inverse problem investigated consists of identifying the geometry of discontinuities in a conductive material from Cauchy data measurements taken on the boundary. Temperature and heat flux are measured on the outside boundary of the domain and the position and the size of a super-elliptical inclusion are determined by minimising an objective functional using an evolution strategy. The super-elliptical form allows the parametric model to More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 69-86, 2006, DOI:10.3970/cmes.2006.015.069

Abstract In this paper we will study the numerical integrations of second order boundary value problems under the imposed conditions at t=0 and t=T in a general setting. We can construct a compact space shooting method for finding the unknown initial conditions. The key point is based on the construction of a one-step Lie group element G(u₀,u_T) and the establishment of a mid-point Lie group element G(r). Then, by imposing G(u₀,u_T) = G(r) we can search the missing initial conditions through an iterative solution of the weighting factor r ∈ (0,1). Numerical examples were examined to convince that the new More >

S. Noroozi¹, P. Sewell¹, J. Vinney¹

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 171-180, 2006, DOI:10.3970/cmes.2006.014.171

Abstract A method that combines a modified back propagation Artificial Neural Network (ANN) and Boundary Element Analysis (BEA) was introduced and discussed in the author's previous papers. This paper discusses the development of an automated inverse boundary element problem engine. This inverse problem engine can be applied to both potential and elastostatic problems.
In this study, BEA solutions of a two-dimensional potential problem is utilised to test the system and to train a back propagation Artificial Neural Network (ANN). Once training is completed and the transfer function is created, the solution to any subsequent or new… More >

L.S. Miers¹, J.C.F. Telles²

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 161-170, 2006, DOI:10.3970/cmes.2006.014.161

Abstract This work aims at extending the concept of the Numerical Green's Function (NGF), well known from boundary element applications to fracture mechanics, to the Local Boundary Integral Equation (LBIE) context. As a "companion" solution, the NGF is used to remove the integrals over the crack boundary and is introduced only for source points whose support touches or contains the crack. The results obtained with the coupling of NGF-LBIE in previous potential discontinuity Laplace's equation problems and the authors' experience in NGF-BEM fracture mechanics were the motivation for this development. More >

L.A. de Lacerda¹, J. M. da Silva¹

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 153-160, 2006, DOI:10.3970/cmes.2006.014.153

Abstract A two-dimensional boundary element formulation is presented and coupled to a genetic algorithm to identify polarization curves of buried slender structures. The dual boundary element method is implemented to model the cathodic protection of the metallic body and the genetic algorithm is employed to deal with the inverse problem of determining the non-linear polarization curve, which describes the relation between current density and electrochemical potential at the soil metal interface. In this work, this non-linear relation resulting from anodic and cathodic reactions is represented by a classical seven parameters expression. Stratified soil resistivity is modeled More >