Algebraic multilevel preconditioning of finite element matrices using local Schur complements

2006 ◽  
Vol 13 (1) ◽  
pp. 49-70 ◽  
Author(s):  
J. K. Kraus
Keyword(s):  
Finite Element ◽  
Schur Complements ◽  
Multilevel Preconditioning

An Optimal Multilevel Method with One Smoothing Step for the Morley Element

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shibing Tang ◽  
Xuejun Xu
Keyword(s):  
Finite Element ◽  
Dirichlet Problem ◽  
Computational Complexity ◽  
Numerical Experiments ◽  
Multilevel Methods ◽  
Multilevel Method ◽  
Morley Element ◽  
Nonconforming Element ◽  
Linear Algebraic Systems ◽  
Multilevel Preconditioning

Abstract In this paper, a class of multilevel preconditioning schemes is presented for solving the linear algebraic systems resulting from the application of Morley nonconforming element approximations to the biharmonic Dirichlet problem. Based on an appropriate space splitting of the finite element spaces associated with the refinements and the abstract Schwarz framework, we prove that the proposed multilevel methods with one smoothing step are optimal, i.e., the convergence rate is independent of the mesh sizes and mesh levels. Moreover, the computational complexity is also optimal since the smoothers are performed only once on each level in the algorithm. Numerical experiments are provided to confirm the optimality of the suggested methods.

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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