A multigrid correction scheme for a new Steklov eigenvalue problem in inverse scattering

ABSTRACT

We propose a multigrid correction scheme to solve a new Steklov eigenvalue problem in inverse scattering. With this scheme, solving an eigenvalue problem in a fine finite element space is reduced to solve a series of boundary value problems in fine finite element spaces and a series of eigenvalue problems in the coarsest finite element space. And the coefficient matrices associated with those linear systems are constructed to be symmetric and positive definite. We prove error estimates of eigenvalues and eigenfunctions. Numerical results coincide in theoretical analysis and indicate our scheme is highly efficient in solving the eigenvalue problem.

KEYWORDS:

• Steklov eigenvalue problem
• multigrid correction
• error estimate
• numerical experiments

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65N25
• 65N30

Acknowledgments

We cordially thank the editor and the referees for their valuable comments and suggestions which led to the improvement of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Nature Science Foundation of China [grant no. 11761022], the project of Young Scientific and Technical Talents Development of Education Department of Guizhou Province [KY [2018]153].