2 research outputs found
A Multilevel Correction Type of Adaptive Finite Element Method for Eigenvalue Problems
A type of adaptive finite element method for the eigenvalue problems is
proposed based on the multilevel correction scheme. In this method, adaptive
finite element method to solve eigenvalue problems involves solving associated
boundary value problems on the adaptive partitions and small scale eigenvalue
problems on the coarsest partitions. Hence the efficiency of solving eigenvalue
problems can be improved to be similar to the adaptive finite element method
for the associated boundary value problems. The convergence and optimal
complexity is theoretically verified and numerically demonstrated.Comment: 36 pages, 16 figure
A Parallel Augmented Subspace Method for Eigenvalue Problems
A type of parallel augmented subspace scheme for eigenvalue problems is
proposed by using coarse space in the multigrid method. With the help of coarse
space in multigrid method, solving the eigenvalue problem in the finest space
is decomposed into solving the standard linear boundary value problems and very
low dimensional eigenvalue problems. The computational efficiency can be
improved since there is no direct eigenvalue solving in the finest space and
the multigrid method can act as the solver for the deduced linear boundary
value problems. Furthermore, for different eigenvalues, the corresponding
boundary value problem and low dimensional eigenvalue problem can be solved in
the parallel way since they are independent of each other and there exists no
data exchanging. This property means that we do not need to do the
orthogonalization in the highest dimensional spaces. This is the main aim of
this paper since avoiding orthogonalization can improve the scalability of the
proposed numerical method. Some numerical examples are provided to validate the
proposed parallel augmented subspace method.Comment: 23 pages, 16 figure