High Performance Numerical Solution of Partial Differential Equations: Richardson Extrapolation-based High Accuracy High Efficiency Computation for Partial Differential Equations - Couverture souple

Dai, Ruxin

 
9783659879654: High Performance Numerical Solution of Partial Differential Equations: Richardson Extrapolation-based High Accuracy High Efficiency Computation for Partial Differential Equations
Couverture souple
ISBN 10 : 3659879657 ISBN 13 : 9783659879654
Editeur : LAP LAMBERT Academic Publishing, 2016

Synopsis

A Richardson extrapolation-based sixth-order method is developed for 2D and 3D steady-state equations on uniform grids. Richardson extrapolation is applied to explicitly compute a sixth-order solution on the coarse grid from two fourth-order solutions with different related scale grids. Other computational techniques (i.e., iterative operator based interpolation, multiple coarse grid updating strategy, and completed Richardson extrapolation) are discussed to obtain a higher-order solution on the fine grid. No extra cost is needed to build such kind of multilevel grids if multigrid methods are involved as the solver for the resulting linear systems. For this reason, a multiscale multigrid method is used to achieve both high accuracy and high efficiency computational goals in one framework. Richardson extrapolation-based computation is also extended to solve unsteady-state equations. A higher-order alternating direction implicit method with completed Richardson extrapolation is developed for solving unsteady 2D convection-diffusion equations. The completed Richardson extrapolation is used to improve the accuracy of the solution in spatial and temporal domains simultaneously.

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Présentation de l'éditeur

A Richardson extrapolation-based sixth-order method is developed for 2D and 3D steady-state equations on uniform grids. Richardson extrapolation is applied to explicitly compute a sixth-order solution on the coarse grid from two fourth-order solutions with different related scale grids. Other computational techniques (i.e., iterative operator based interpolation, multiple coarse grid updating strategy, and completed Richardson extrapolation) are discussed to obtain a higher-order solution on the fine grid. No extra cost is needed to build such kind of multilevel grids if multigrid methods are involved as the solver for the resulting linear systems. For this reason, a multiscale multigrid method is used to achieve both high accuracy and high efficiency computational goals in one framework. Richardson extrapolation-based computation is also extended to solve unsteady-state equations. A higher-order alternating direction implicit method with completed Richardson extrapolation is developed for solving unsteady 2D convection-diffusion equations. The completed Richardson extrapolation is used to improve the accuracy of the solution in spatial and temporal domains simultaneously.

Biographie de l'auteur

Ruxin Dai is an assistant professor of Computer Science at University of Wisconsin River Falls. She obtained her PhD from University of Kentucky in 2014. Her research interests include finite difference methods, multigrid methods, and numerical algorithms for solving partial differential equations.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2016
Langue
anglais
ISBN 10 
3659879657
ISBN 13 
9783659879654
Reliure
Broché
Nombre de pages
188
Coordonnées du fabricant
non disponible
Personne responsable
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