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A New Multigrid Finite Element Method for the Transmission Eigenvalue Problems

Research paper by Jiayu Han, Yidu Yang, Hai Bi

Indexed on: 11 Jan '16Published on: 11 Jan '16Published in: Mathematics - Numerical Analysis



Abstract

Numerical methods for the transmission eigenvalue problems are hot topics in recent years. Based on the work of Lin and Xie [Math. Comp., 84(2015), pp. 71-88], we build a multigrid method to solve the problems. With our method, we only need to solve a series of primal and dual eigenvalue problems on a coarse mesh and the associated boundary value problems on the finer and finer meshes. Theoretical analysis and numerical results show that our method is simple and easy to implement and is efficient for computing real and complex transmission eigenvalues.