CMES-Vol. 37, No. 3, 2008

Open Access

ARTICLE

Stable MFS Solution to Singular Direct and Inverse Problems Associated with the Laplace Equation Subjected to Noisy Data
LiviuMarin ¹
CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 203-242, 2008, DOI:10.3970/cmes.2008.037.203
Abstract In this paper, a meshless method for the stable solution of direct and inverse problems associated with the two-dimensional Laplace equation in the presence of boundary singularities and noisy boundary data is proposed. The governing equation and boundary conditions are discretized by the method of fundamental solutions (MFS), whilst the existence of the boundary singularity is taken into account by subtracting from the original MFS solution the corresponding singular solutions, as given by the asymptotic expansion of the solution near the singular point. However, even in the case when the boundary singularity is accounted for, More >

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Scattering of flexural wave in thin plate with multiple holes by using the null-field integral equation approach
Wei-Ming Lee¹, Jeng-Tzong Chen^2,3
CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 243-273, 2008, DOI:10.3970/cmes.2008.037.243
Abstract In this paper, a semi-analytical approach is proposed to solve the scattering problem of flexural waves and to determine dynamic moment concentration factors (DMCFs) in an infinite thin plate with multiple circular holes. The null-field integral formulation is employed in conjunction with degenerate kernels, tensor transformation and Fourier series. In the proposed direct formulation, all dynamic kernels of plate are expanded into degenerate forms and further the rotated degenerate kernels have been derived for the general exterior problem. By uniformly collocating points on the real boundary, a linear algebraic system is constructed. The results of… More >

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A Variational Formulation of a Stabilized Unsplit Convolutional Perfectly Matched Layer for The Isotropic or Anisotropic Seismic Wave Equation
R. Martin¹, D. Komatitsch^1,2, S. D. Gedney³
CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 274-304, 2008, DOI:10.3970/cmes.2008.037.274
Abstract In the context of the numerical simulation of seismic wave propagation, the perfectly matched layer (PML) absorbing boundary condition has proven to be efficient to absorb surface waves as well as body waves with non grazing incidence. But unfortunately the classical discrete PML generates spurious modes traveling and growing along the absorbing layers in the case of waves impinging the boundary at grazing incidence. This is significant in the case of thin mesh slices, or in the case of sources located close to the absorbing boundaries or receivers located at large offset. In previous work… More >

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The Coupling Method of Natural Boundary Element and Mixed Finite Element for Stationary Navier-Stokes Equation in Unbounded Domains
Dongjie Liu¹, Dehao Yu²
CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 305-330, 2008, DOI:10.3970/cmes.2008.037.305
Abstract The coupling method of natural boundary element and mixed finite element is applied to analyze the stationary Navier-Stokes equation in 2-D unbounded domains. After an artificial smooth boundary is introduced, the original nonlinear problem is reduced into an equivalent problem defined in bounded computational domain. The well-posedness of the reduced problem is proved. The finite element approximation of this problem is given, and numerical example is provided to show the feasibility and efficiency of the method. More >

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