scholarly journals Two-parameter homogenization for a nonlinear periodic Robin problem for the Poisson equation: a functional analytic approach

2017 ◽  
Vol 31 (1) ◽  
pp. 63-110 ◽  
Author(s):  
Massimo Lanza de Cristoforis ◽  
Paolo Musolino
Keyword(s):  
Poisson Equation ◽  
Analytic Approach ◽  
Robin Problem ◽  
The Poisson Equation ◽  
Two Parameter

scholarly journals Asymptotic Behaviour of the Energy Integral of a Two-Parameter Homogenization Problem with Nonlinear Periodic Robin Boundary Conditions

2019 ◽  
Vol 62 (4) ◽  
pp. 985-1016 ◽  
Author(s):  
Massimo Lanza de Cristoforis ◽  
Paolo Musolino
Keyword(s):  
Relative Size ◽  
Homogenization Theory ◽  
Perforated Domain ◽  
Positive Parameter ◽  
Robin Problem ◽  
Energy Integral ◽  
Homogenization Problem ◽  
The Poisson Equation ◽  
Robin Boundary ◽  
Two Parameter

AbstractWe consider a nonlinear Robin problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δ. The relative size of each periodic perforation is determined by a positive parameter ε. Under suitable assumptions, such a problem admits a family of solutions which depends on ε and δ. We analyse the behaviour the energy integral of such a family as (ε, δ) tends to (0, 0) by an approach that represents an alternative to asymptotic expansions and classical homogenization theory.

On Green’s function of the Robin problem for the Poisson equation

2019 ◽  
Vol 10 (3) ◽  
pp. 203-213 ◽  
Author(s):  
Valery V. Karachik ◽  
Batirkhan K. Turmetov
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Unit Ball ◽  
Poisson Equation ◽  
Green's Function ◽  
Explicit Representation ◽  
Robin Problem ◽  
The Poisson Equation ◽  
The Green Function

AbstractAn explicit representation of the Green function of the Robin problem for the Poisson equation in the unit ball is given.

scholarly journals Modified iterative method with red-black ordering for image composition using poisson equation

2021 ◽  
Vol 10 (4) ◽  
pp. 2016-2027
Author(s):  
Zakariah Aris ◽  
Nordin Saad ◽  
A’qilah Ahmad Dahalan ◽  
Andang Sunarto ◽  
Azali Saudi
Keyword(s):  
Poisson Equation ◽  
Linear Equations ◽  
Numerical Differentiation ◽  
Laplacian Operator ◽  
Source Image ◽  
Relaxation Methods ◽  
Image Composition ◽  
The Poisson Equation ◽  
Speed Up ◽  
Two Parameter

Image composition involves the process of embedding a selected region of the source image to the target image to produce a new desirable image seamlessly. This paper presents an image composition procedure based on numerical differentiation using the laplacian operator to obtain the solution of the poisson equation. The proposed method employs the red-black strategy to speed up the computation by using two acceleration parameters. The method is known as modified two-parameter over-relaxation (MTOR) and is an extension of the existing relaxation methods. The MTOR was extensively studied in solving various linear equations, but its usefulness in image processing was never explored. Several examples were tested to examine the effectiveness of the proposed method in solving the poisson equation for image composition. The results showed that the proposed MTOR performed faster than the existing methods.

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