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1.
Andreas Karageorghis 《Journal of scientific computing》1991,6(1):21-26
The way boundary conditions are imposed when applying Chebyshev collocation methods to Poisson and biharmonic-type problems in rectangular domains is investigated. It is shown that careful selection of the number of collocation points leads to a linear system ofn linearly independent equations inn unknowns. 相似文献
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The current distribution and overall polarization behavior of electrodeposition at a flow-through (packed bed or fluidized bed) electrode are modeled by means of a one-dimensional model involving a primary reacting species and a simultaneous side reaction. The model equations are solved by orthogonal collocation; the time and storage requirements compare favorably to those of finite-difference methods. Experimental data obtained using a packed-bed electrode are compared with the model predictions and various methods of fitting the data are compared. 相似文献
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A Chebyshev collocation strategy is introduced for the subdivision of cuboids into cuboidal subdomains (elements). These elements are conforming, which means that the approximation to the solution isC
0 continuous at all points across their interfaces. 相似文献
5.
针对模拟移动床(SMB)综合速率模型,采用有限元法和正交配点法分别对柱向和颗粒径向模型进行离散化,利用MatLab ODE求解器对SMB过程进行数值求解。通过仿真,验证了该方法的可行性。 相似文献
6.
Collocation methods are developed for the solution of some differential equation models for transport phenomena problems in one-and two-dimensions in co-axial annuli of spherical and cylindrical shapes. General formulae are developed to obtain orthogonal polynomials over an arbitrary interval using two types of weighting functions. The convergence and accuracy of the methods are demonstrated using two test problems, i.e., calculation of effectiveness factors in (a) a spherical pellet with peripherally deposited catalyst and (b) a Raschig ring type cylindrical catalyst pellet. Comparisons of results obtained from the present methods with analytic solutions for the first-order reactions indicate good agreement. Numerical solutions are also obtained for the second-and the third-order reactions for which analytic solutions are not available. Results obtained in terms of a new Thiele modulus involving the ratio of volume of peripherally deposited part of catalyst to exterior surface area indicate that this normalization brings effectiveness factor versus Thiele modulus curves close together for co-axial spherical and long cylindrical pellets, as it does for these geometries without the inner co-axial portion. 相似文献
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Zhongying Chen Shengpei Ding Hongqi Yang 《Computers & Mathematics with Applications》2011,62(4):2071-2082
This paper continues the theme of the recent work Chen et al. (2008) [18], in which fast collocation methods are introduced for solving ill-posed Fredholm integral equations of the first kind. We develop in this paper multilevel augmentation algorithms, which lead to fast solutions of the discrete equations resulting from fast collocation methods. Regularization parameter choice strategies are given for proposed methods. The theoretical analysis and numerical experiments illustrate the accuracy and efficiency of the algorithm. 相似文献
10.
Geometrically non-linear behavior of structural systems with random material property: An asymptotic spectral stochastic approach 总被引:1,自引:0,他引:1
M. Tootkaboni L. Graham-Brady B.W. Schafer 《Computer Methods in Applied Mechanics and Engineering》2009,198(37-40):3173-3185
An asymptotic spectral stochastic approach is presented for computing the statistics of the equilibrium path in the post-bifurcation regime for structural systems with random material properties. The approach combines numerical implementation of Koiter’s asymptotic theory with a stochastic Galerkin scheme and collocation in stochastic space to quantify uncertainties in the parametric representation of the load–displacement relationship, specifically in the form of uncertain post-buckling slope, post-buckling curvature, and a family of stochastic displacement fields. Using the proposed method, post-buckling response statistics for two plane frames are obtained and shown to be in close agreement with those obtained from Monte Carlo simulation, provided a fine enough spectral representation is used to model the variability in the random dimension. 相似文献