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

Ruxin Dai

ISBN 10: 3659879657 / ISBN 13: 9783659879654

Published by LAP LAMBERT Academic Publishing, 2016

About this Item

188 pages. 8.66x5.91x0.43 inches. In Stock.

Seller Inventory # 3659879657

Bibliographic Details

• Title: High Performance Numerical Solution of Partial Differential Equations: Richardson Extrapolation-based High Accuracy High Efficiency Computation for Partial Differential Equations
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2016
• Language: English
• ISBN 10: 3659879657
• ISBN 13: 9783659879654
• Binding: Paperback
• Condition: Brand New
• Weight: 0.33 kilograms

About this title

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.

About the Author

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.