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Ludmil Drenchev Jerzy Sobczak Rajiv Asthana Savko Malinov 《Journal of Computer-Aided Materials Design》2003,10(1):35-54
Ordered porosity metal materials belong to a relatively new class of porous materials named gasars. This paper presents a mathematical model of the complex physical phenomena in the production of gasars. Analyses for heat transfer, solidification kinetics and gas diffusion were coupled to describe the formation of unique gasar structure. Several criterial functions were introduced to provide significant quantitative information about the relationship between the operating technological parameters and the final structure. The computational outcomes of the numerical simulation were compared with the characteristics of real gasar ingots. The model was applied to determine the boundary conditions that would provide approximately constant physical conditions on the solidification front. The structure sensitiveness of gasars with respect to the different technological parameters is discussed. 相似文献
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This paper is devoted to the study of an energy minimizing basis first introduced in Wan, Chan and Smith (2000) for algebraic multigrid methods. The basis will be first obtained in an explicit and compact form in terms of certain local and global operators. The basis functions are then proved to be locally harmonic functions on each coarse grid element. Using these new results, it is illustrated that this basis can be numerically obtained in an optimal fashion. In addition to the intended application for algebraic multigrid method, the energy minimizing basis may also be applied for numerical homogenization. 相似文献
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We consider the discrete system resulting from mixed finite element approximation of a second-order elliptic boundary value problem with Crouzeix–Raviart non-conforming elements for the vector valued unknown function and piece-wise constants for the scalar valued unknown function. Since the mass matrix corresponding to the vector valued variables is diagonal, these unknowns can be eliminated exactly. Thus, the problem of designing an efficient algorithm for the solution of the resulting algebraic system is reduced to one of constructing an efficient algorithm for a system whose matrix is a graph-Laplacian (or weighted graph-Laplacian). 相似文献
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Blanca Ayuso de Dios Franco Brezzi L. Donatella Marini Jinchao Xu Ludmil Zikatanov 《Journal of scientific computing》2014,58(3):517-547
In this paper we construct Discontinuous Galerkin approximations of the Stokes problem where the velocity field is $H(\mathrm{div},\Omega )$ -conforming. This implies that the velocity solution is divergence-free in the whole domain. This property can be exploited to design a simple and effective preconditioner for the final linear system. 相似文献
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Paola F. Antonietti Marco Sarti Marco Verani Ludmil T. Zikatanov 《Journal of scientific computing》2017,70(2):608-630
In this paper we design and analyze a uniform preconditioner for a class of high-order Discontinuous Galerkin schemes. The preconditioner is based on a space splitting involving the high-order conforming subspace and results from the interpretation of the problem as a nearly-singular problem. We show that the proposed preconditioner exhibits spectral bounds that are uniform with respect to the discretization parameters, i.e., the mesh size, the polynomial degree and the penalization coefficient. The theoretical estimates obtained are supported by numerical tests. 相似文献
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The recently introduced circulant block-factorization preconditioners are studied in this paper. The general approach is first formulated for the case of block-tridiagonal sparse matrices. Then an estimate of the condition number of the preconditioned matrix for a model anisotropic Dirichlet boundary value problem is derived in the formκ<√2ε(n+1)+2, whereN=n 2 is the size of the discrete problem, andε stands for the ratio of the anisotropy. Various numerical tests demonstrating the behavior of the circulant block-factorization preconditioners for anisotropic problems are presented. 相似文献
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<正>Functionally graded materials,including their characterization,properties and production methods are a new rapidly developing field of materials science.The aims of this review are to systematize the basic production techniques for manufacturing functionally graded materials.Attention is paid to the principles for obtaining graded structure mainly in the metal based functionally graded materials.Several unpublished results obtained by the authors have been discussed briefly.Experimental methods and theoretical analysis for qualitative and quantitative estimation of graded properties have also been presented.The article can be useful for people who work in the field of functionally graded structures and materials,and who need a compact informative review of recent experimental and theoretical activity in this area. 相似文献
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In the development of high fidelity transport solvers, optimization of the use of available computational resources and access to a tool for assessing quality of the solution are key to the success of large-scale nuclear systems’ simulation. In this regard, error control provides the analyst with a confidence level in the numerical solution and enables for optimization of resources through Adaptive Mesh Refinement (AMR). 相似文献
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We present iterative and preconditioning techniques for the solution of the linear systems resulting from several discontinuous Galerkin (DG) Interior Penalty (IP) discretizations of elliptic problems. We analyze the convergence properties of these algorithms for both symmetric and non-symmetric IP schemes. The iterative methods are based on a “natural” decomposition of the first order DG finite element space as a direct sum of the Crouzeix-Raviart non-conforming finite element space and a subspace that contains functions discontinuous at interior faces. We also present numerical examples confirming the theoretical results. 相似文献
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