A highly efficient H1-Galerkin mixed finite element method （MFEM） is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation ...A highly efficient H1-Galerkin mixed finite element method （MFEM） is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O（h^2） for both the original variable u in H1 （Ω） norm and the flux p = u in H（div, Ω） norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O（h^3） are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.展开更多
采用Mortar有限单元法(mortar finite element method,MFEM)能够得到正定、对称的系数矩阵,而且刚度矩阵是分块对称的,这种特点适合于并行迭代求解。阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了适合...采用Mortar有限单元法(mortar finite element method,MFEM)能够得到正定、对称的系数矩阵,而且刚度矩阵是分块对称的,这种特点适合于并行迭代求解。阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了适合于NO-MFEM并行计算的区域分解策略以及并行求解的基本流程。针对简单2维静电场问题,使用NO-MFEM进行了并行计算,并与理论值和串行计算结果进行对比,验证了所提方法的有效性。同时,对于非协调网格造成的计算误差进行了分析。NO-MFEM法的并行计算为工程应用中优化设计问题的区域分解和并行求解提供了一种新的选择。展开更多
Mortar元法(mortar element method,MEM)是一种新型区域分解算法,它允许将求解区域分解为多个子域,在各个区域以最适合子域特征的方式离散。在各个区域的交界面上,边界节点不要求逐点匹配,而是通过建立加权积分形式的Mortar条件使得交...Mortar元法(mortar element method,MEM)是一种新型区域分解算法,它允许将求解区域分解为多个子域,在各个区域以最适合子域特征的方式离散。在各个区域的交界面上,边界节点不要求逐点匹配,而是通过建立加权积分形式的Mortar条件使得交界面上的传递条件在分布意义上满足。Mortar有限元法(mortar finite element method,MFEM)将MEM和有限元法(finite element method,FEM)相结合,在各区域中分别使用FEM网格离散,区域的交界面上通过施加Mortar条件实现区域间的自由度连续。该文阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了NO-MFEM的程序实现过程,使用NO-MFEM对2维静磁场问题和3维静电场问题进行了计算,并与FEM模型结果进行对比,验证了该文方法的有效性。将NO-MFEM应用于电磁分析,丰富了电磁场数值计算理论,为运动涡流问题和大规模问题的分析提供了新的选择。展开更多
The lowest order H1-Galerkin mixed finite element method （for short MFEM） is proposed for a class of nonlinear sine-Gordon equations with the simplest bilinear rectangular element and zero order Raviart- Thomas elem...The lowest order H1-Galerkin mixed finite element method （for short MFEM） is proposed for a class of nonlinear sine-Gordon equations with the simplest bilinear rectangular element and zero order Raviart- Thomas element. Base on the interpolation operator instead of the traditional Ritz projection operator which is an indispensable tool in the traditional FEM analysis, together with mean-value technique and high accuracy analysis, the superclose properties of order O（h2）/O（h2 ＋ r2） in Hi-norm and H（div; Ω）-norm axe deduced for the semi-discrete and the fully-discrete schemes, where h, r- denote the mesh size and the time step, respectively, which improve the results in the previous literature.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.10971203,11271340,and 11101381)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101110006)
文摘A highly efficient H1-Galerkin mixed finite element method （MFEM） is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O（h^2） for both the original variable u in H1 （Ω） norm and the flux p = u in H（div, Ω） norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O（h^3） are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.
文摘采用Mortar有限单元法(mortar finite element method,MFEM)能够得到正定、对称的系数矩阵,而且刚度矩阵是分块对称的,这种特点适合于并行迭代求解。阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了适合于NO-MFEM并行计算的区域分解策略以及并行求解的基本流程。针对简单2维静电场问题,使用NO-MFEM进行了并行计算,并与理论值和串行计算结果进行对比,验证了所提方法的有效性。同时,对于非协调网格造成的计算误差进行了分析。NO-MFEM法的并行计算为工程应用中优化设计问题的区域分解和并行求解提供了一种新的选择。
文摘Mortar元法(mortar element method,MEM)是一种新型区域分解算法,它允许将求解区域分解为多个子域,在各个区域以最适合子域特征的方式离散。在各个区域的交界面上,边界节点不要求逐点匹配,而是通过建立加权积分形式的Mortar条件使得交界面上的传递条件在分布意义上满足。Mortar有限元法(mortar finite element method,MFEM)将MEM和有限元法(finite element method,FEM)相结合,在各区域中分别使用FEM网格离散,区域的交界面上通过施加Mortar条件实现区域间的自由度连续。该文阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了NO-MFEM的程序实现过程,使用NO-MFEM对2维静磁场问题和3维静电场问题进行了计算,并与FEM模型结果进行对比,验证了该文方法的有效性。将NO-MFEM应用于电磁分析,丰富了电磁场数值计算理论,为运动涡流问题和大规模问题的分析提供了新的选择。
基金Supported in part by the National Natural Science Foundation of China under Grant Nos.11671369,11271340the Natural Science Foundation of the Education Department of Henan Province under Grant Nos.14A110009,16A110022
文摘The lowest order H1-Galerkin mixed finite element method （for short MFEM） is proposed for a class of nonlinear sine-Gordon equations with the simplest bilinear rectangular element and zero order Raviart- Thomas element. Base on the interpolation operator instead of the traditional Ritz projection operator which is an indispensable tool in the traditional FEM analysis, together with mean-value technique and high accuracy analysis, the superclose properties of order O（h2）/O（h2 ＋ r2） in Hi-norm and H（div; Ω）-norm axe deduced for the semi-discrete and the fully-discrete schemes, where h, r- denote the mesh size and the time step, respectively, which improve the results in the previous literature.
