Numerical zoom for advection diffusion problems with localized multiscales

We investigate the Schwarz'domain decomposition algorithm for numerical zooms. Error estimates are given for nonmatching meshes for elliptic and parabolic partial differential equations. The method is applied to the security assessment of the burial of nuclear waste which is a typical multiscale problem for porous media flow. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

球面上第二类Fredholm积分方程配置方法

球面上第二类 Fredholm积分方程经球坐标变换可化为矩形域 H0 上的问题求解 .用有限元法构造H0 上的插值函数 ,它必须满足在 H0 的左、右两边连续 ,然后用配置方程求方程的近似解     

Analysis for Transmission Characteristics of Closed Trapezoidal-Groove Waveguide with Boundary Element Method

In this paper, the cut-off and dispersion characteristics of a new kind of closed trapezoidal-groove waveguide that has more advantages than open groove waveguides are analyzed with the help of the boundary element method, the relationship between cut-off wavelengths and variations of guide's relative sizes is discussed in detail. The calculated results are in good agreement with those in the relevant reference. So, the obtained conclusions are very important in theoretical studies and actual applications of closed trapezoidal-groove waveguides for millimeter and submillimeter waves.     

New mixed finite elements for plane elasticity and Stokes equations

We consider mixed finite elements for the plane elasticity system and the Stokes equation. For the unmodified Hellinger-Reissner formulation of elasticity in which the stress and displacement fields are the primary unknowns, we derive two new nonconforming mixed finite elements of triangle type. Both elements use piecewise rigid motions to approximate the displacement and piecewise polynomial functions to approximate the stress, where no vertex degrees of freedom are involved. The two stress finite element ...     

A new domain decomposition method with overlapping patches for ultrascale simulations: Application to biological flows

We address the failure in scalability of large-scale parallel simulations that are based on (semi-)implicit time-stepping and hence on the solution of linear systems on thousands of processors. We develop a general algorithmic framework based on domain decomposition that removes the scalability limitations and leads to optimal allocation of available computational resources. It is a non-intrusive approach as it does not require modification of existing codes. Specifically, we present here a two-stage domain decomposition method for the Navier–Stokes equations that combines features of discontinuous and continuous Galerkin formulations. At the first stage the domain is subdivided into overlapping patches and within each patch a C⁰ spectral element discretization (second stage) is employed. Solution within each patch is obtained separately by applying an efficient parallel solver. Proper inter-patch boundary conditions are developed to provide solution continuity, while a Multilevel Communicating Interface (MCI) is developed to provide efficient communication between the non-overlapping groups of processors of each patch. The overall strong scaling of the method depends on the number of patches and on the scalability of the standard solver within each patch. This dual path to scalability provides great flexibility in balancing accuracy with parallel efficiency. The accuracy of the method has been evaluated in solutions of steady and unsteady 3D flow problems including blood flow in the human intracranial arterial tree. Benchmarks on BlueGene/P, CRAY XT5 and Sun Constellation Linux Cluster have demonstrated good performance on up to 96,000 cores, solving up to 8.21B degrees of freedom in unsteady flow problem. The proposed method is general and can be potentially used with other discretization methods or in other applications.     

Boundary element method for calculation of effective elastic moduli in 3D linear elasticity

A boundary integral formulation of the linear elasticity problem for a multi‐component composite is given. The fast BEM solver based on the adaptive cross approximation is then obtained by the data‐sparse representation of the resulting Galerkin matrices. The solver is used to obtain effective elastic moduli of fibre and particle reinforced composites in three dimensions by means of the strain energy equivalence principle. Copyright © 2009 John Wiley & Sons, Ltd.     

A finite strain contact model for mixed lubricated surfaces in forming processes

For an accurate simulation of forming processes, it is of paramount importance to model the different lubrication regimes that can develop at the contact interface. These might vary from zone to zone of the forming piece, and from one regime to another, resulting in forces of different nature and magnitude. In these cases, the use of the classical Coulomb friction law will be clearly not sufficient to capture, in a suitable manner, the variety of forces applied on the forming piece.     

二阶Dirichlet问题的三维等参元逼近及其数值积分格式

本文研究了求解三维二阶Drichlet问题的四面体等参元逼近格式.基于对等参变换的细致估计,证明了格式的收敛性,并得到了H~1-误差的最优估计.为简化等参元的复杂计算,本文还构造了一种简单的数值积分格式,并证明了其收敛性.     

A POSTERIORI ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF THE CAHN-HILLIARD EQUATION AND THE HELE-SHAW FLOW

This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation ut ＋ △（ε△Au-ε^-1f（u）） = 0. It is shown that the a posteriori error bounds depends on ε^-1 only in some low polynomial order, instead of exponential order. Using these a posteriori error estimates, we construct at2 adaptive algorithm for computing the solution of the Cahn- Hilliard equation and its sharp interface limit, the Hele-Shaw flow. Numerical experiments are presented to show the robustness and effectiveness of the new error estimators and the proposed adaptive algorithm.