A Conservative Domain Decomposition Procedure for Nonlinear Diffusion Problems on Arbitrary Quadrilateral Grids

2011 ◽  
Vol 33 (3) ◽  
pp. 1352-1368 ◽  
Author(s):  
Guangwei Yuan ◽  
Yanzhong Yao ◽  
Li Yin
Keyword(s):  
Domain Decomposition ◽  
Nonlinear Diffusion ◽  
Decomposition Procedure ◽  
Conservative Domain ◽  
Diffusion Problems

scholarly journals Instability of Traveling Pulses in Nonlinear Diffusion-Type Problems and Method to Obtain Bottom-Part Spectrum of Shrödinger Equation with Complicated Potential

2021 ◽  
Author(s):  
Michael I. Tribelsky
Keyword(s):  
Ground State ◽  
Nonlinear Diffusion ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations ◽  
Dinger Equation ◽  
Bottom Part ◽  
Diffusion Type ◽  
Traveling Pulses ◽  
General Method ◽  
Diffusion Problems

The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically the problem is reduced to the calculation of the "energy" of the ground state in Schrödinger equation with a complicated potential. A general method to obtain the bottom-part spectrum of such equations based on the approximation of the potential by square wells is proposed and applied. Possible generalization of the approach to other types of nonlinear diffusion equations is discussed.

COMPARISON BETWEEN GLOBAL, CLASSICAL DOMAIN DECOMPOSITION AND LOCAL, SINGLE AND DOUBLE COLLOCATION METHODS BASED ON RBF INTERPOLATION FOR SOLVING CONVECTION-DIFFUSION EQUATION

2008 ◽  
Vol 19 (11) ◽  
pp. 1737-1751 ◽  
Author(s):  
GAIL GUTIERREZ ◽  
WHADY FLOREZ
Keyword(s):  
Diffusion Equation ◽  
Domain Decomposition ◽  
Mixed Boundary ◽  
Domain Decomposition Method ◽  
Collocation Methods ◽  
Special Treatment ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Full Domain ◽  
Diffusion Problems

This work presents a performance comparison of several meshless RBF formulations for convection-diffusion equation with moderate-to-high Peclet number regimes. For the solution of convection-diffusion problems, several comparisons between global (full-domain) meshless RBF methods and mesh-based methods have been presented in the literature. However, in depth studies between new local RBF collocation methods and full-domain symmetric RBF collocation methods are not reported yet. The RBF formulations included: global symmetric method, symmetric double boundary collocation method, additive Schwarz domain decomposition method (DDM) when it is incorporated into two anterior approaches, and local single and double collocation methods. It can be found that the accuracy of solutions deteriorates as Pe increases, if no special treatment is used. From the numerical tests, it seems that the local methods, especially the derived double collocation technique incorporating PDE operator, are more effective than full domain approaches even with iterative DDM in solving moderate-to-high Pe convection-diffusion problems subject to mixed boundary conditions.

scholarly journals Approximate solutions to a new class of nonlinear diffusion problems

1999 ◽  
Vol 108 (1-2) ◽  
pp. 219-231 ◽  
Author(s):  
Alberto Cabada ◽  
Juan J. Nieto ◽  
Rodrigo L. Pouso
Keyword(s):  
Nonlinear Diffusion ◽  
Approximate Solutions ◽  
New Class ◽  
Diffusion Problems
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