Implementation of the Finite Element Method with Optimal Choice of Basic Functions for Dirichlet Problem for Poisson Equation

2015 ◽  
Vol 47 (9) ◽  
pp. 42-62
Author(s):  
Oleg N. Lytvyn ◽  
Konstantin V. Nosov ◽  
Tatyana A. Baranova
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dirichlet Problem ◽  
Poisson Equation ◽  
Optimal Choice ◽  
The Finite Element Method ◽  
Basic Functions ◽  
Element Method

scholarly journals Approximation Solution For Nonlinear Poisson Equation By Finite Element_Homotopy Method: الحل التقريبي لمعادلة بواسون غير الخطية بطريقة هوموتوبي_العناصر المنتهية FE_HM

2020 ◽  
Vol 4 (2) ◽  
Author(s):  
Hiba Zakaria Aslan, Habib Solaiman Ali, Berlant Sabri Mattit
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Poisson Equation ◽  
Homotopy Analysis Method ◽  
Nonlinear Partial Differential Equations ◽  
Analysis Method ◽  
The Finite Element Method ◽  
Approximation Solution ◽  
Homotopy Analysis ◽  
Element Method

The main aim to this research is to find the approximation solution of the nonlinear Poisson equation by combining the finite element method FEM with homotopy analysis method HAM in a single approximation method because the finite element method needs when applied to nonlinear partial differential equations either for iterative methods such as ( Newton_Gauss Method14, Picard's iterative method3, Newton_Galarkin Method4) or for other approximation methods such as(B_Splain24, Homotopy Analysis6). In this article, the finite element method was combined with the Homotopy analysis method with one method called Homotopy _Finite Element Method FE_HM, to convert the nonlinear matter into a linear matter through the HAM method, and to overcome the engineering complexity of the region by a grid of finite elements through the FEM method, We obtained good results when applying this method to the nonlinear Poisson equation on Dirichlet boundary condition, and this method was programmed through the Matlab program.

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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