scholarly journals Fast Iterative Solution of Reaction-Diffusion Control Problems Arising from Chemical Processes

2013 ◽  
Vol 35 (5) ◽  
pp. B987-B1009 ◽  
Author(s):  
John W. Pearson ◽  
Martin Stoll
Keyword(s):  
Reaction Diffusion ◽  
Iterative Solution ◽  
Chemical Processes ◽  
Diffusion Control ◽  
Control Problems

A BGK MODEL FOR CHEMICAL PROCESSES: THE REACTION-DIFFUSION APPROXIMATION

1994 ◽  
Vol 04 (01) ◽  
pp. 35-47 ◽  
Author(s):  
RENATO SPIGLER ◽  
DAMIÁN H. ZANETTE
Keyword(s):  
Kinetic Model ◽  
Diffusion Approximation ◽  
Reaction Diffusion ◽  
Chemical Processes ◽  
Reaction Diffusion Equations ◽  
The Other ◽  
Diffusion Equations ◽  
Bgk Model ◽  
Chemical Substances ◽  
Chemical Effects

A BGK-type kinetic model is derived for describing the interaction of chemical substances. The ensuing equation is then solved asymptotically on certain space-time scales on which an appreciable interplay between kinetic and chemical effects, or the prevailing of one on the other, can be observed. The description of the interaction at the macroscopic level consists of a hierarchy of reaction-diffusion equations satisfied by the densities. Comparison is made with similar results previously obtained from certain phenomenological models, and illustrative examples are given.

scholarly journals Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks

2020 ◽  
Vol 146 (2) ◽  
pp. 335-368
Author(s):  
Owe Axelsson ◽  
János Karátson
Keyword(s):  
Optimal Control ◽  
Rate Of Convergence ◽  
Large Scale ◽  
Optimal Control Problems ◽  
Iterative Solution ◽  
Control Problems ◽  
Block Form ◽  
Solution Methods ◽  
Preconditioned Matrix ◽  
Iterative Solution Methods

Abstract Matrices or operators in two-by-two block form with square blocks arise in numerous important applications, such as in optimal control problems for PDEs. The problems are normally of very large scale so iterative solution methods must be used. Thereby the choice of an efficient and robust preconditioner is of crucial importance. Since some time a very efficient preconditioner, the preconditioned square block, PRESB method has been used by the authors and coauthors in various applications, in particular for optimal control problems for PDEs. It has been shown to have excellent properties, such as a very fast and robust rate of convergence that outperforms other methods. In this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs. Under certain conditions, the condition number of the preconditioned matrix is bounded by 2 or even smaller. Furthermore, under certain assumptions the rate of convergence is superlinear.

scholarly journals Robust Iterative Solution of a Class of Time-Dependent Optimal Control Problems

PAMM ◽  
2012 ◽  
Vol 12 (1) ◽  
pp. 3-6 ◽  
Author(s):  
John W. Pearson ◽  
Martin Stoll ◽  
Andrew J. Wathen
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Iterative Solution ◽  
Time Dependent ◽  
Control Problems

scholarly journals Reaction-diffusion control in somitogenesis

2001 ◽  
Vol 41 (supplement) ◽  
pp. S186
Author(s):  
J. Ozaki ◽  
M. Hirata ◽  
S. Kondo
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Control

scholarly journals Analysis of the Boundary Value and Control Problems for Nonlinear Reaction–Diffusion–Convection Equation

2001 ◽  
Vol 14 (4) ◽  
pp. 452-462
Author(s):  
Gennady V. Alekseev ◽  
Keyword(s):  
Boundary Value Problem ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Reaction Diffusion ◽  
Control Problems ◽  
Stability Estimates ◽  
Convection Equation ◽  
Reaction Coefficient ◽  
Diffusion Convection ◽  
And Control

The global solvability of the inhomogeneous mixed boundary value problem and control problems for the reaction–diffusion–convection equation are proved in the case when the reaction coefficient nonlinearly depends on the concentration. The maximum and minimum principles are established for the solution of the boundary value problem. The optimality systems are derived and the local stability estimates of optimal solutions are established for control problems with specific reaction coefficients

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