CMES-Vol. 15, No. 3, 2006

Open Access

ARTICLE

Local Defect Correction for the Boundary Element Method
G. Kakuba¹, R.M.M. Mattheij², M.J.H. Anthonissen³
CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 127-136, 2006, DOI:10.3970/cmes.2006.015.127
Abstract This paper presents an efficient way to implement the Boundary Element Method (BEM) to capture high activity regions in a boundary value problem. In boundary regions where accuracy is critical, like in adaptive surface meshes, the method of choice is Local Defect Correction (LDC). We formulate the method and demonstrate its applicability and reliability by means of an example. Numerical results show that LDC and BEM together provide accurate solutions with less computational requirements given that BEM systems usually consist of dense matrices. More >

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ARTICLE

Performance of Multiquadric Collocation Method in Solving Lid-driven Cavity Flow Problem with Low Reynolds Number
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 >

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Remeshing and Refining with Moving Finite Elements. Application to Nonlinear Wave Problems
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 >

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Efficient Green's Function Modeling of Line and Surface Defects in Multilayered Anisotropic Elastic and Piezoelectric Materials¹
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 >

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ARTICLE

The Lie-Group Shooting Method for Singularly Perturbed Two-Point Boundary Value Problems
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 >

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