求解第一类二次棱元方程的快速迭代法

Fast Iiterative Method for Solving First Family Quadratic Edge Finite Element Equations

针对正定Maxwell方程组的第一类Ndlec二次棱有限元方程,通过建立棱有限元空间的一种新的稳定性分解,设计了求解棱元方程组的快速迭代算法,并且在理论上严格证明了该迭代算法的收敛率不依赖于网格的规模.数值实验验证了理论的正确性.

In this paper, we design a fast iterative method for a first family of Nédélec quadratic edge finite element equations of the positive definite Maxwell＇s equations, this is done by a new stable decomposition of the edge finite elements space. By strict theoretical analysis, we prove that the convergent rate of iterative method is independent of mesh size. Numerical experiments confirm the theoretical results.