Error Estimating Code (EEC) is a new channel coding method to estimate the Bit Error Rate (BER) information of the transmitted sequence. However, the estimated BER is not precise enough if the practical value of BER i...Error Estimating Code (EEC) is a new channel coding method to estimate the Bit Error Rate (BER) information of the transmitted sequence. However, the estimated BER is not precise enough if the practical value of BER is high. A weighted EEC estimation method is proposed to improve the accuracy performance of BER estimation by classifying the raw estimation results into intervals and multiplying them by different coefficients separately. The applications of weighted EEC in modulation selection scheme and distributed video coding are discussed. Simulation results show that the EEC-based modulation selection method can achieve better performance at a cost of little redundancy and computation, and the EEC-based rate estimation method in distributed video coding can save the decoding time.展开更多
To provide a iheoreiical basis for h-type .finire elemenl analysis with quadrilateralelements, in the present paper, the h-convergence of quadrilateral elements is established. whose related lemmas and theorems being ...To provide a iheoreiical basis for h-type .finire elemenl analysis with quadrilateralelements, in the present paper, the h-convergence of quadrilateral elements is established. whose related lemmas and theorems being presented, and therefore, theerror estimate problems are investigated.展开更多
In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Un...In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Unlike the biharmonic operator A2, the bi-wave operator □^2 is not an elliptic operator, so the energy space for the bi-wave equation is much larger than the energy space for the biharmonic equation. This then makes it possible to construct low order conforming finite elements for the bi-wave equation. However, the existence and construction of such finite elements strongly depends on the mesh. In the paper, we first characterize mesh conditions which allow and not allow construction of low order conforming finite elements for approximating the bi-wave equation. We then construct a cubic and a quartic conforming finite element. It is proved that both elements have the desired approximation properties, and give optimal order error estimates in the energy norm, suboptimal （and optimal in some cases） order error estimates in the H1 and L^2 norm. Finally, numerical experiments are presented to guage the efficiency of the proposed finite element methods and to validate the theoretical error bounds.展开更多
In this paper, using a bubble function, we construct a cuboid element to solve the fourth order elliptic singular perturbation problem in three dimensions. We prove that the nonconforming CO-cuboid element converges i...In this paper, using a bubble function, we construct a cuboid element to solve the fourth order elliptic singular perturbation problem in three dimensions. We prove that the nonconforming CO-cuboid element converges in the energy norm uniformly with respect to the perturbation parameter.展开更多
This paper develops and analyzes multigrid semismooth Newton methods for a class of inequality-constrained optimization problems in function space which are motivated by and include linear elastic contact problems of ...This paper develops and analyzes multigrid semismooth Newton methods for a class of inequality-constrained optimization problems in function space which are motivated by and include linear elastic contact problems of Signorini type. We show that after a suitable Moreau-Yosida type regularization of the problem superlinear local convergence is obtained for a class of semismooth Newton methods. In addition, estimates for the order of tile error introduced by the regularization are derived. The main part of the paper is devoted to the analysis of a multilevel preconditioner for the semismooth Newton system. We prove a rigorous bound for the contraction rate of the multigrid cycle which is robust with respect to sufficiently small regularization parameters and the number of grid levels. Moreover, it applies to adaptively refined grids. The paper concludes with numerical results.展开更多
This paper proposes and analyzes a class of robust globally divergence-free weak Galerkin （WG） finite element methods for Stokes equations. The new methods use the Pk/Pk-1 （k ≥ 1） discontinuous finite element com...This paper proposes and analyzes a class of robust globally divergence-free weak Galerkin （WG） finite element methods for Stokes equations. The new methods use the Pk/Pk-1 （k ≥ 1） discontinuous finite element combination for velocity and pressure in the interior of elements, and piecewise P1/Pk （l = k - 1, k） for the trace approximations of the ve- locity and pressure on the inter-element boundaries. Our methods not only yield globally divergence-free velocity solutions, but also have uniform error estimates with respect to the Reynolds number. Numerical experiments are provided to show the robustness of the proposed methods.展开更多
基金Supported by the Nation Natural Science Foundation of China(11472063)the Provincial Natural Science Research Program of Higher Education Institutions of Anhui Province(KJ2013A194,KJ2013Z230)Anhui Province Colleges and Universities Outstanding Youth Talent Support Program(gxyq ZD2016285)
基金supported bythe 111 Project under Grant No. B08004the major project of Ministry of Industry and Information Technology of the People's Republic of China under Grant No. 2010ZX03002-006China Fundamental Research Funds for the Central Universities
文摘Error Estimating Code (EEC) is a new channel coding method to estimate the Bit Error Rate (BER) information of the transmitted sequence. However, the estimated BER is not precise enough if the practical value of BER is high. A weighted EEC estimation method is proposed to improve the accuracy performance of BER estimation by classifying the raw estimation results into intervals and multiplying them by different coefficients separately. The applications of weighted EEC in modulation selection scheme and distributed video coding are discussed. Simulation results show that the EEC-based modulation selection method can achieve better performance at a cost of little redundancy and computation, and the EEC-based rate estimation method in distributed video coding can save the decoding time.
文摘To provide a iheoreiical basis for h-type .finire elemenl analysis with quadrilateralelements, in the present paper, the h-convergence of quadrilateral elements is established. whose related lemmas and theorems being presented, and therefore, theerror estimate problems are investigated.
基金partially supported by the NSF grant DMS-0710831
文摘In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Unlike the biharmonic operator A2, the bi-wave operator □^2 is not an elliptic operator, so the energy space for the bi-wave equation is much larger than the energy space for the biharmonic equation. This then makes it possible to construct low order conforming finite elements for the bi-wave equation. However, the existence and construction of such finite elements strongly depends on the mesh. In the paper, we first characterize mesh conditions which allow and not allow construction of low order conforming finite elements for approximating the bi-wave equation. We then construct a cubic and a quartic conforming finite element. It is proved that both elements have the desired approximation properties, and give optimal order error estimates in the energy norm, suboptimal （and optimal in some cases） order error estimates in the H1 and L^2 norm. Finally, numerical experiments are presented to guage the efficiency of the proposed finite element methods and to validate the theoretical error bounds.
文摘In this paper, using a bubble function, we construct a cuboid element to solve the fourth order elliptic singular perturbation problem in three dimensions. We prove that the nonconforming CO-cuboid element converges in the energy norm uniformly with respect to the perturbation parameter.
文摘This paper develops and analyzes multigrid semismooth Newton methods for a class of inequality-constrained optimization problems in function space which are motivated by and include linear elastic contact problems of Signorini type. We show that after a suitable Moreau-Yosida type regularization of the problem superlinear local convergence is obtained for a class of semismooth Newton methods. In addition, estimates for the order of tile error introduced by the regularization are derived. The main part of the paper is devoted to the analysis of a multilevel preconditioner for the semismooth Newton system. We prove a rigorous bound for the contraction rate of the multigrid cycle which is robust with respect to sufficiently small regularization parameters and the number of grid levels. Moreover, it applies to adaptively refined grids. The paper concludes with numerical results.
文摘This paper proposes and analyzes a class of robust globally divergence-free weak Galerkin （WG） finite element methods for Stokes equations. The new methods use the Pk/Pk-1 （k ≥ 1） discontinuous finite element combination for velocity and pressure in the interior of elements, and piecewise P1/Pk （l = k - 1, k） for the trace approximations of the ve- locity and pressure on the inter-element boundaries. Our methods not only yield globally divergence-free velocity solutions, but also have uniform error estimates with respect to the Reynolds number. Numerical experiments are provided to show the robustness of the proposed methods.
