Local And Parallel Finite Element Algorithms For Eigenvalue Problems With Homogeneous Mixed Boundary Conditions

Local and parallel finite element algorithms is one of the most important methods for the numerical solution of partial differential equations. On the basis of local algorithm, Xu and Zhou put forward this method at the first time in 2000. From then on, many scientific workers do a lot of work for the algorithm on theory, and obtained abundant achievements.It is very important for local and parallel algorithms to choose a proper local domain.Usually,the first way is solving directly, and then we draw the solution of the 3 dimension graphics by using computer, observe the case of sudden change. At last, we select the obvious abrupt change domain as the local domain to refine. Based on the work of Xu and Zhou [Math. Comp., 69(2000), pp. 881-909], this paper discusses two types of local and parallel algorithms for eigenvalue problems with homogeneous mixed boundary conditions.Theoretical analysis and numerical experiments show that the discussed algorithms in this paper are efficient for eigenvalue problems with homogeneous mixed boundary conditions.In the numerical experiment section, by comparing the solution of the algorithms in this paper with the solution of the traditional finite element method, we can obtain the results that verify our theory. The algorithms are performed under the package of iFEM, and satisfactory results are obtained.