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| 1 | A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection显示文摘Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods.This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection.This algorithm is used in PHG,Parallel Hierarchical Grid (http://gffzz8065c2988e934515h0vk660c6vfwx60bb.ffgz.tsg.suse.edu.cn/phg/),a toolbox under active development for parallel adaptive finite element solutions of partial differential equations.The algorithm proposed is characterized by allowing simultaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices.Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given,which is useful in better understanding the behaviour of the bisectioning refinement procedure. | Lin-Bo Zhang | 2009 | Numerical Mathematics(Theory,Methods and Applications)2009，2，1： | 27 |
| 2 | Superconvergence of a Nonconforming Finite Element Approximation to Viscoelasticity Type Equations on Anisotropic Meshes显示文摘The main aim of this paper is to study the approximation to viscoelasticity type equations with a Crouzeix-Raviart type nonconforming finite element on the anisotropic meshes. The superclose property of the exact solution and the optimal error estimate of its derivative with respect to time are derived by using some novel techniques. Moreover, employing a postprocessing technique, the global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is studied. | Dongyang Shi Yucheng Peng Shaochun Chen | 2006 | Numerical Mathematics A Journal of Chinese Universities(English Series)2006，15，4： | 21 |
| 3 | A Globally Convergent Polak-Ribiere-Polyak Conjugate Gradient Method with Armijo-Type Line Search显示文摘In this paper, we propose a globally convergent Polak-Ribiere-Polyak (PRP) conjugate gradient method for nonconvex minimization of differentiable functions by employing an Armijo-type line search which is simpler and less demanding than those defined in [4,10]. A favorite property of this method is that we can choose the initial stepsize as the one-dimensional minimizer of a quadratic modelΦ(t):= f(xk)+tgkTdk+(1/2) t2dkTQkdk, where Qk is a positive definite matrix that carries some second order information of the objective function f. So, this line search may make the stepsize tk more easily accepted. Preliminary numerical results show that this method is efficient. | Gaohang Yu Lutai Guan Zengxin Wei | 2006 | Numerical Mathematics A Journal of Chinese Universities(English Series)2006，15，4： | 11 |
| 4 | Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations显示文摘The block-by-block method,proposed by Linz for a kind of Volterra integral equations with nonsingular kernels,and extended by Kumar and Agrawal to a class of initial value problems of fractional differential equations(FDEs)with Caputo derivatives,is an efficient and stable scheme.We analytically prove and numerically verify that this method is convergent with order at least 3 for any fractional order indexα>0. | Jianfei Huang Yifa Tang Luis Vázquez | 2012 | Numerical Mathematics(Theory,Methods and Applications)2012，5，2： | 11 |
| 5 | Fast Texture Segmentation Based on Semi-Local Region Descriptor and Active Contour显示文摘In this paper,we present an efficient approach for unsupervised segmentation of natural and textural images based on the extraction of image features and a fast active contour segmentation model.We address the problem of textures where neither the gray-level information nor the boundary information is adequate for object extraction.This is often the case of natural images composed of both homogeneous and textured regions.Because these images cannot be in general directly processed by the gray-level information,we propose a new texture descriptor which intrinsically defines the geometry of textures using semi-local image information and tools from differential geometry.Then,we use the popular Kullback-Leibler distance to design an active contour model which distinguishes the background and textures of interest.The existence of a minimizing solution to the proposed segmentation model is proven.Finally, a texture segmentation algorithm based on the Split-Bregman method is introduced to extract meaningful objects in a fast way.Promising synthetic and real-world results for gray-scale and color images are presented. | Nawal Houhou Jean-Philippe Thiran Xavier Bresson | 2009 | Numerical Mathematics(Theory,Methods and Applications)2009，2，4： | 10 |
| 6 | A Nonconforming Arbitrary Quadrilateral Finite Element Method for Approximating Maxwell's Equations显示文摘The main aim of this paper is to provide convergence analysis of Quasi-Wilson nonconforming finite element to Maxwell's equations under arbitrary quadrilateral meshes.The error estimates are derived,which are the same as those for conforming elements under conventional regular meshes. | Dongyang Shi Lifang Pei Shaochun Chen | 2007 | Numerical Mathematics A Journal of Chinese Universities(English Series)2007，16，4： | 9 |
| 7 | GENERALIZED MATRIX MULTISPLITTING RELAXATION METHODS AND THEIR CONVERGENCE显示文摘In this paper, we set up a general framework of parallel matrix mullisplitting relaxation methods for solving large scale system of linear equations. We investigate the convergence properties of this framework and give several sufficient conditions ensuring it to converge as well as diverge. At last, we conclude a necessary and sufficient condition for the convergence of this framework when the coefficient matrix is an L-matrix. | 白中治 王德人 | 1993 | Numerical Mathematics A Journal of Chinese Universities(English Series)1993，2，1： | 8 |
| 8 | COMPUTATION OF VECTOR VALUED BLENDING RATIONAL INTERPOLANTS显示文摘As we know, Newton's interpolation polynomial is based on divided differ-ences which can be calculated recursively by the divided-difference scheme while Thiele'sinterpolating continued fractions are geared towards determining a rational functionwhich can also be calculated recursively by so-called inverse differences. In this paper,both Newton's interpolation polynomial and Thiele's interpolating continued fractionsare incorporated to yield a kind of bivariate vector valued blending rational interpolantsby means of the Samelson inverse. Blending differences are introduced to calculate theblending rational interpolants recursively, algorithm and matrix-valued case are dis-cussed and a numerical example is given to illustrate the efficiency of the algorithm. | 檀结庆 | 2003 | Numerical Mathematics A Journal of Chinese Universities(English Series)2003，12，1： | 8 |
| 9 | A CONDITIONAL STABILITY FOR AN INVERSE PROBLEM ARISING IN GROUNDWATER POLLUTION显示文摘An inverse problem of determining magnitude of groundwater pollution in a hydrologic region is investigated. By applying integral identity methods, a conditional stability for the inverse problem here is constructed with aids of an optimal adjoint problem and a suitable topology. | 李功胜 谭永基 | 2005 | Numerical Mathematics A Journal of Chinese Universities(English Series)2005，14，3： | 7 |
| 10 | A New Homotopy Method for Nonlinear Complementarity Problems显示文摘In this paper, we present a new homotopy method for the nonlinear complementarity problems. Without the regularity or non-singulary assumptions for▽F(x), we prove that our homotopy equations have a bounded solution curve. The numerical tests confirm the efficiency of our proposed method. | Jundi Ding Hongyou Yin | 2007 | Numerical Mathematics A Journal of Chinese Universities(English Series)2007，16，2： | 6 |
| 11 | Advances in Studies and Applications of Centroidal Voronoi Tessellations显示文摘Centroidal Voronoi tessellations(CVTs) have become a useful tool in many applications ranging from geometric modeling,image and data analysis,and numerical partial differential equations,to problems in physics,astrophysics,chemistry,and biology. In this paper,we briefly review the CVT concept and a few of its generalizations and well-known properties.We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs.Whenever possible,we point out some outstanding issues that still need investigating. | Qiang Du Max Gunzburger Lili Ju | 2010 | Numerical Mathematics(Theory,Methods and Applications)2010，3，2： | 6 |
| 12 | THE FINITE DIFFERENCE STREAMLINE DIFFUSION METHODS FOR TIME-DEPENDENT CONVECTION-DIFFUSION EQUATIONS显示文摘In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L^2-norm. | 孙澈 沈慧 | 1998 | Numerical Mathematics A Journal of Chinese Universities(English Series)1998，7，1： | 6 |
| 13 | On the Approximation of the Derivatives of Spline Quasi-Interpolation in Cubic Spline Space S_(3)^(1,2)(∆_(mn)^((2)))显示文摘In this paper,based on the basis composed of two sets of splines with distinct local supports,cubic spline quasi-interpolating operators are reviewed on nonuniform type-2 triangulation.The variation diminishing operator is defined by discrete linear functionals based on a fixed number of triangular mesh-points,which can reproduce any polynomial of nearly best degrees.And by means of the modulus of continuity,the estimation of the operator approximating a real sufficiently smooth function is reviewed as well.Moreover,the derivatives of the nearly optimal variation diminishing operator can approximate that of the real sufficiently smooth function uniformly over quasi-uniform type-2 triangulation.And then the convergence results are worked out. | Jiang Qian Fan Wang | 2014 | Numerical Mathematics(Theory,Methods and Applications)2014，7，1： | 6 |
| 14 | A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization显示文摘This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function.We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function.Under a local Lipschitzian error bound assumption,we show that the algorithm possesses global and local linear convergence properties.We also give some numerical tests(including image recovery examples) to illustrate the efficiency of the proposed method. | Zheng-Jian Bai Michael K. Ng Liqun Qi | 2009 | Numerical Mathematics(Theory,Methods and Applications)2009，2，4： | 6 |
| 15 | BIVARIATE VECTOR VALUED RATIONAL INTERPOLANTS BY BRANCHED CONTINUED FRACTIONS显示文摘By making use of Thiele-type bivariate branched continued fractions and Sumelson inverse,we construct a few kinds of bivariate vector valued rational interpolonts (BVRIs) over rectangular grids and find out certain relations among these BVRIs such as boundary identity and duality. | 檀结庆 朱功勤 | 1995 | Numerical Mathematics A Journal of Chinese Universities(English Series)1995，4，1： | 5 |
| 16 | A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation显示文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results. | Ningning Yan Zhaojie Zhou | 2008 | Numerical Mathematics(Theory,Methods and Applications)2008，1，3： | 5 |
| 17 | A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations显示文摘In this paper,we propose a compound algorithm for the image restoration. The algorithm is a convex combination of the ROF model and the LET model with a parameter functionθ.The numerical experiments demonstrate that our compound algorithm is efficient and preserves the main advantages of the two models.In particular, the errors of the compound algorithm in L2 norm between the exact images and corresponding restored images are the smallest among the three models.For images with strong noises,the restored images of the compound algorithm are the best in the corresponding restored images.The proposed algorithm combines the fixed point method, an improved AMG method and the Krylov acceleration.It is found that the combination of these methods is efficient and robust in the image restoration. | Qianshun Chang Xuecheng Tai Lily Xing | 2009 | Numerical Mathematics(Theory,Methods and Applications)2009，2，4： | 5 |
| 18 | The Simultaneous Approximation Average Errors for Bernstein Operators on the r-Fold Integrated Wiener Space显示文摘For weighted approximation in Lp-norm,we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the r-fold integrated Wiener space. | Guiqiao Xu | 2012 | Numerical Mathematics(Theory,Methods and Applications)2012，5，3： | 5 |
| 19 | Superconvergence and L^(∞)-Error Estimates of RT1Mixed Methods for Semilinear Elliptic Control Problems with an Integral Constraint显示文摘In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral constraint.The state and co-state are approximated by the order one Raviart-Thomas mixed finite element space and the control variable is approximated by piecewise constant functions or piecewise linear functions.We derive some superconvergence results for the control variable and the state variables when the control is approximated by piecewise constant functions.Moreover,we derive L∞-error estimates for both the control variable and the state variables when the control is discretized by piecewise linear functions.Finally,some numerical examples are given to demonstrate the theoretical results. | Yanping Chen Tianliang Hou | 2012 | Numerical Mathematics(Theory,Methods and Applications)2012，5，3： | 5 |
| 20 | PARAMETER IDENTIFICATION PROBLEM OF THE FRACTAL INTERPOLATION FUNCTIONS显示文摘Parameter identification problem is one of essential problem in order to model effectively experimental data by fractal interpolation function.In this paper,we first present an example to explain a relationship between iteration procedure and fractal function.Then we discuss conditions that vertical scaling factors must obey in one typical case. | 阮火军 沙震 苏维宜 | 2003 | Numerical Mathematics A Journal of Chinese Universities(English Series)2003，12，2： | 4 |
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