CMES-Vol. 84, No. 2, 2012

Open Access

ARTICLE

Gauss Process Based Approach for Application on Landslide Displacement Analysis and Prediction
Zaobao Liu^1,2, Weiya Xu¹, Jianfu Shao²
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 99-122, 2012, DOI:10.3970/cmes.2012.084.099
Abstract In this paper, the Gauss process is proposed for application on landslide displacement analysis and prediction with dynamic crossing validation. The prediction problem using noisy observations is first introduced. Then the Gauss process method is proposed for modeling non-stationary series of landslide displacements based on its ability to model noisy data. The monitoring displacement series of the New Wolong Temple Landslide is comparatively studied with other methods as an instance to implement the strategy of the Gauss process for predicting landslide displacement. The dynamic crossing validation method is adopted to manage the displacement series so as to give more precise… More >

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ARTICLE

Solving Nonlinear Solid Mechanics Problems with theJacobian-Free Newton Krylov Method
J. D. Hales¹, S. R. Novascone¹, R. L. Williamson¹, D. R. Gaston¹, M. R. Tonks¹
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 123-154, 2012, DOI:10.3970/cmes.2012.084.123
Abstract The equations governing solid mechanics are often solved via Newton's method. This approach can be problematic if the Jacobian determination, storage, or solution cost is high. These challenges are magnified for multiphysics applications. The Jacobian-free Newton-Krylov (JFNK) method avoids many of these difficulties through a finite difference approximation. A parallel, nonlinear solid mechanics and multiphysics application named BISON has been created that leverages JFNK. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and multiphysics applications using a series of demonstration problems. We show that JFNK has distinct advantages in many cases. More >

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Application of Homotopy Analysis Method for Periodic Heat Transfer in Convective Straight Fins with Temperature-Dependent Thermal Conductivity
Wei-Chung Tien¹, Yue-Tzu Yang¹, Cha’o-Kuang Chen^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 155-170, 2012, DOI:10.3970/cmes.2012.084.155
Abstract In this paper, the homotopy analysis method is applied to analyze the heat transfer of the oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. This method is a powerful and easy-to-use tool for non-linear problems and it provides us with a simple way to adjust and control the convergence region of solution series. Without the need of iteration, the obtained solution is in the form of an infinite power series and the results indicated that the series has high accuracy by comparing it with those generated by the complex combination method. More >

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Several Compact Local Stencils based on Integrated RBFs for Fourth-Order ODEs and PDEs
T.-T. Hoang-Trieu¹, N. Mai-Duy¹, T. Tran-Cong¹
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 171-204, 2012, DOI:10.3970/cmes.2012.084.171
Abstract In this paper, new compact local stencils based on integrated radial basis functions (IRBFs) for solving fourth-order ordinary differential equations (ODEs) and partial differential equations (PDEs) are presented. Five types of compact stencils - 3-node and 5-node for 1D problems and 5×5-node, 13-node and 3×3 -node for 2D problems - are implemented. In the case of 3-node stencil and 3×3-node stencil, nodal values of the first derivative(s) of the field variable are treated as additional unknowns (i.e. 2 unknowns per node for 3-node stencil and 3 unknowns per node for 3×3-node stencil). The integration constants arising from the construction of… More >

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