full multigrid method
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Author(s):  
Manting Xie ◽  
Fei Xu ◽  
Meiling Yue

In this paper, a type of full multigrid method is proposed to solve non-selfadjoint Steklov eigenvalue problems. Multigrid iterations for corresponding selfadjoint and positive definite boundary value problems generate proper iterate solutions that are subsequently added to the coarsest finite element space in order to improve approximate eigenpairs on the current mesh. Based on this full multigrid, we propose a new type of adaptive finite element method for non-selfadjoint Steklov eigenvalue problems. We prove that the computational work of these new schemes are almost optimal, the same as solving the corresponding positive definite selfadjoint boundary value problems. In this case, these type of iteration schemes certainly improve the overfull efficiency of solving the non-selfadjoint Steklov eigenvalue problem. Some numerical examples are provided to validate the theoretical results and the efficiency of this proposed scheme.


2020 ◽  
Vol 37 (1) ◽  
pp. 444-461
Author(s):  
Fei Xu ◽  
Qiumei Huang ◽  
Hongkun Ma

IEEE Access ◽  
2020 ◽  
pp. 1-1
Author(s):  
Mohamed A. Abouelatta ◽  
Sayed A. Ward ◽  
Ahmad M. Sayed ◽  
Karar Mahmoud ◽  
Matti Lehtonen ◽  
...  

2018 ◽  
Vol 24 (3) ◽  
pp. 884-901 ◽  
Author(s):  
Kunihide Ohashi ◽  
Takanori Hino ◽  
Hiroshi Kobayashi ◽  
Naoyuki Onodera ◽  
Nobuaki Sakamoto

2017 ◽  
Vol 10 (3) ◽  
pp. 639-655 ◽  
Author(s):  
M. M. Butt ◽  
Y. Yuan

AbstractA full multigrid method with coarsening by a factor-of-three to distributed control problems constrained by Stokes equations is presented. An optimal control problem with cost functional of velocity and/or pressure tracking-type is considered with Dirichlet boundary conditions. The optimality system that results from a Lagrange multiplier framework, form a linear system connecting the state, adjoint, and control variables. We investigate multigrid methods with finite difference discretization on staggered grids. A coarsening by a factor-of-three is used on staggered grids that results nested hierarchy of staggered grids and simplified the inter-grid transfer operators. A distributive-Gauss-Seidel smoothing scheme is employed to update the state- and adjoint-variables and a gradient update step is used to update the control variables. Numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed multigrid framework to tracking-type optimal control problems.


2016 ◽  
Vol 322 ◽  
pp. 747-759 ◽  
Author(s):  
Hongtao Chen ◽  
Hehu Xie ◽  
Fei Xu

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