An efficient parallel iteration algorithm for nonlinear diffusion equations with time extrapolation techniques and the Jacobi explicit scheme

2021 ◽  
pp. 110435
Author(s):  
Shuai Miao ◽  
Yanzhong Yao ◽  
Guixia Lv
Keyword(s):  
Nonlinear Diffusion ◽  
Explicit Scheme ◽  
Diffusion Equations ◽  
Iteration Algorithm ◽  
Nonlinear Diffusion Equations ◽  
Parallel Iteration ◽  
Time Extrapolation

A Conservative Parallel Iteration Scheme for Nonlinear Diffusion Equations on Unstructured Meshes

2016 ◽  
Vol 20 (5) ◽  
pp. 1405-1423 ◽  
Author(s):  
Yunlong Yu ◽  
Yanzhong Yao ◽  
Guangwei Yuan ◽  
Xingding Chen
Keyword(s):  
Domain Decomposition ◽  
Nonlinear Diffusion ◽  
Domain Decomposition Method ◽  
Iteration Scheme ◽  
Diffusion Equations ◽  
Finite Volume Scheme ◽  
Nonlinear Diffusion Equations ◽  
Speed Up ◽  
Parallel Iteration ◽  
Prediction Approach

AbstractIn this paper, a conservative parallel iteration scheme is constructed to solve nonlinear diffusion equations on unstructured polygonal meshes. The design is based on two main ingredients: the first is that the parallelized domain decomposition is embedded into the nonlinear iteration; the second is that prediction and correction steps are applied at subdomain interfaces in the parallelized domain decomposition method. A new prediction approach is proposed to obtain an efficient conservative parallel finite volume scheme. The numerical experiments show that our parallel scheme is second-order accurate, unconditionally stable, conservative and has linear parallel speed-up.

scholarly journals The Neumann problem for nonlocal nonlinear diffusion equations

2007 ◽  
Vol 8 (1) ◽  
pp. 189-215 ◽  
Author(s):  
Fuensanta Andreu ◽  
José M. Mazón ◽  
Julio D. Rossi ◽  
Julián Toledo
Keyword(s):  
Neumann Problem ◽  
Nonlinear Diffusion ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations ◽  
The Neumann Problem ◽  
Nonlocal Nonlinear

scholarly journals Conditional Lie-Bäcklund Symmetries and Reductions of the Nonlinear Diffusion Equations with Source

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Junquan Song ◽  
Yujian Ye ◽  
Danda Zhang ◽  
Jun Zhang
Keyword(s):  
Invariant Subspace ◽  
Dynamic Systems ◽  
Nonlinear Diffusion ◽  
Invariant Subspaces ◽  
Higher Order ◽  
Diffusion Equations ◽  
Canonical Forms ◽  
Nonlinear Diffusion Equations ◽  
Symmetry Approach ◽  
Finite Dimensional

Conditional Lie-Bäcklund symmetry approach is used to study the invariant subspace of the nonlinear diffusion equations with sourceut=e−qx(epxP(u)uxm)x+Q(x,u),m≠1. We obtain a complete list of canonical forms for such equations admit multidimensional invariant subspaces determined by higher order conditional Lie-Bäcklund symmetries. The resulting equations are either solved exactly or reduced to some finite-dimensional dynamic systems.

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