| Preconditioners for higher order edge finite element discretizations of Maxwell's equations |
| |
| 摘 要： | In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's equations.We present the preconditioners for the first family and second family of higher order N′ed′elec element equations,respectively.By combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning,we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform grids.We also present some numerical experiments to demonstrate the theoretical results.
|
Preconditioners for higher order edge finite element discretizations of Maxwell’s equations |
| |
| Authors: | LiuQiang Zhong Shi Shu DuDu Sun Lin Tan |
| |
| Affiliation: | 1.School of Mathematical and Computational Sciences,Xiangtan University,Xiangtan,China;2.Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Xiangtan,China;3.Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Graduate University of Chinese Academy of Sciences,Chinese Academy Sciences,Beijing,China;4.Department of Math-Physics,Nanhua University,Hengyang,China |
| |
| Abstract: | In this paper, we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell’s equations.
We present the preconditioners for the first family and second family of higher order Nédélec element equations, respectively.
By combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space
preconditioning, we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform
grids. We also present some numerical experiments to demonstrate the theoretical results. |
| |
| Keywords: | preconditioner higher order edge finite element stable decomposition |
| 本文献已被 SpringerLink 等数据库收录！ |
|
