Multiscale Discretization Scheme Based on the Rayleigh Quotient Iterative Method for the Steklov Eigenvalue Problem
نویسندگان
چکیده
This paper discusses efficient numerical methods for the Steklov eigenvalue problem and establishes a new multiscale discretization scheme and an adaptive algorithm based on the Rayleigh quotient iterative method. The efficiency of these schemes is analyzed theoretically, and the constants appeared in the error estimates are also analyzed elaborately. Finally, numerical experiments are provided to support the theory.
منابع مشابه
Bound Constrained Regularization for Ill-Posed Problems
We consider large scale ill-conditioned linear systems arising from discretization of ill-posed problems. Regularization is imposed through an (assumed known) upper bound constraint on the solution. An iterative scheme, requiring the computation of the smallest eigenvalue and corresponding eigenvector, is used to determine the proper level of regularization. In this paper we consider several co...
متن کاملA Block Rayleigh Quotient Iteration with Local Quadratic Convergence
We present an iterative method, based on a block generalization of the Rayleigh Quotient Iteration method, to search for the p lowest eigenpairs of the generalized matrix eigenvalue problem Au = Bu. We prove its local quadratic convergence when B A is symmetric. The benefits of this method are the well-conditioned linear systems produced and the ability to treat multiple or nearly degenerate ei...
متن کاملA two-grid discretization scheme for the Steklov eigenvalue problem
In the paper, a two-grid discretization scheme is discussed for the Steklov eigenvalue problem. With the scheme, the solution of the Steklov eigenvalue problem on a fine grid is reduced to the solution of the Steklov eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. Using spectral approximation theory, it is shown theoretically that the tw...
متن کاملRayleigh Quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves
We show that for the non-Hermitian eigenvalue problem simplified Jacobi-Davidson with preconditioned Galerkin-Krylov solves is equivalent to inexact Rayleigh quotient iteration where the preconditioner is altered by a simple rank one change. This extends existing equivalence results to the case of preconditioned iterative solves. Numerical experiments are shown to agree with the theory.
متن کاملTwo-grid Discretization Schemes of the Nonconforming Fem for Eigenvalue Problems
This paper extends the two-grid discretization scheme of the conforming finite elements proposed by Xu and Zhou (Math. Comput., 70 (2001), pp.17-25) to the nonconforming finite elements for eigenvalue problems. In particular, two two-grid discretization schemes based on Rayleigh quotient technique are proposed. By using these new schemes, the solution of an eigenvalue problem on a fine mesh is ...
متن کامل