Treffer: Higher order optimization and adaptive numerical solution for optimal control of monodomain equations in cardiac electrophysiology

Title:
Higher order optimization and adaptive numerical solution for optimal control of monodomain equations in cardiac electrophysiology
Authors:
NAGAIAH, Chamakuri, KUNISCH, Karl
Source:
Applied numerical mathematics. 61(1):53-65
Publisher Information:
Kidlington: Elsevier, 2011.
Publication Year:
2011
Physical Description:
print, 26 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Optimisation et calcul variationnel numériques, Numerical methods in optimization and calculus of variations, Algorithme, Algorithm, Algoritmo, Analyse numérique, Numerical analysis, Análisis numérico, Calcul variationnel, Variational calculus, Cálculo de variaciones, Commande adaptative, Adaptive control, Control adaptativo, Commande optimale, Optimal control, Control óptimo, Convergence, Convergencia, Equation dérivée partielle, Partial differential equation, Ecuación derivada parcial, Equation réaction diffusion, Reaction diffusion equation, Ecuación reacción difusión, Maillage, Grid pattern, Celdarada, Mathématiques appliquées, Applied mathematics, Matemáticas aplicadas, Méthode Newton, Newton method, Método Newton, Méthode adaptative, Adaptive method, Método adaptativo, Méthode discrétisation, Discretization method, Método discretización, Méthode numérique, Numerical method, Método numérico, Méthode optimisation, Optimization method, Método optimización, Méthode raffinement, Refinement method, Método afinamiento, Optimisation sous contrainte, Constrained optimization, Optimización con restricción, Programmation mathématique, Mathematical programming, Programación matemática, Propagation onde, Wave propagation, Propagación onda, Solution numérique, Numerical solution, Solution optimale, Optimal solution, Solución óptima, 35K57, 35XX, 49J30, 49K30, 49XX, 58A25, 58C15, 65K10, 65Kxx, Adaptive FEM, Monodomain model, Newton's optimization algorithm, PDE constraint optimization, Reaction-diffusion equations
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36, Graz, A-8010, Austria
ISSN:
0168-9274
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=23432834
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.23432834
Database:
PASCAL Archive

Weitere Informationen

In this work adaptive and high resolution numerical discretization techniques are demonstrated for solving optimal control of the monodomain equations in cardiac electrophysiology. A monodomain model, which is a well established model for describing the wave propagation of the action potential in the cardiac tissue, will be employed for the numerical experiments. The optimal control problem is considered as a PDE constrained optimization problem. We present an optimal control formulation for the monodomain equations with an extra-cellular current as the control variable which must be determined in such a way that excitations of the transmembrane voltage are damped in an optimal manner. The focus of this work is on the development and implementation of an efficient numerical technique to solve an optimal control problem related to a reaction-diffusions system arising in cardiac electrophysiology. Specifically a Newton-type method for the monodomain model is developed. The numerical treatment is enhanced by using a second order time stepping method and adaptive grid refinement techniques. The numerical results clearly show that super-linear convergence is achieved in practice.