A multigrid correction scheme for a new Steklov eigenvalue problem in inverse scattering
For researchers working on eigenvalue problems in inverse scattering, this provides an efficient computational method.
The paper proposes a multigrid correction scheme for a new Steklov eigenvalue problem in inverse scattering, reducing fine-space eigenvalue problems to coarse-space eigenvalue problems and fine-space boundary value problems. Numerical results confirm high efficiency.
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.