33 citations · 55 across the 9 of their papers we have counts for
9 papers
An hp-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem
Jiayu Han, Zhimin Zhang
An hp-version interior penalty discontinuous Galerkin (IPDG) method under nonconforming meshes is proposed to solve the quad-curl eigenvalue problem. We prove well-posedness of the…
Spurious solutions for high order curl problems
Kaibo Hu, Qian Zhang, Jiayu Han +2
We investigate numerical solutions of high order curl problems with various formulations and finite elements. We show that several classical conforming finite elements lead to spur…
Value-Gradient based Formulation of Optimal Control Problem and Machine Learning Algorithm
Alain Bensoussan, Jiayue Han, Sheung Chi Phillip Yam +1
Optimal control problem is typically solved by first finding the value function through Hamilton-Jacobi equation (HJE) and then taking the minimizer of the Hamiltonian to obtain th…
Multigrid methods based on shifted inverse iteration for the Maxwell eigenvalue problem
Jiayu Han
In this paper two types of multgrid methods, i.e., the Rayleigh quotient iteration and the inverse iteration with fixed shift, are developed for solving the Maxwell eigenvalue prob…
A New Multigrid Finite Element Method for the Transmission Eigenvalue Problems
Jiayu Han, Yidu Yang, Hai Bi
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…
Non-conforming finite element methods for transmission eigenvalue problem
Yidu Yang, Jiayu Han, Hai Bi
The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem…
An -conforming spectral element method on multi-dimensional domain and its application to transmission eigenvalues
Jiayu Han, Yidu Yang
In this paper we develop an -conforming () spectral element method on multi-dimensional domain associated with the partition into multi-dimensional rectangles. We const…
Error estimates and a two grid scheme for approximating transmission eigenvalues
Yidu Yang, Jiayu Han, Hai Bi
In this paper, using the linearization technique we write the Helmholtz transmission eigenvalue problem as an equivalent nonselfadjoint linear eigenvalue problem whose left-hand si…
The Multilevel Finite Element Discretizations Based on Local Defect-Correction for Nonsymmetric Eigenvalue Problems
Yidu Yang, Jiayu Han
Based on the work of Xu and Zhou [Math.Comput., 69(2000), pp.881-909], we establish new three-level and multilevel finite element discretizations by local defect-correction techniq…