Extending and Automating Fourier Analysis for Multigrid Methods

Derivate 7380

1.45 MB in one file, last changed at 22.01.2018

File list / details

FileFiles changed onSize
dc1729.pdf22.01.2018 13:31:481.45 MB

In this thesis, we develop a general framework for local Fourier analysis of multigrid methods that is versatile and well suited for computer implementation.

Using this framework we are able to analyze multigrid methods which have not been considered to this point. We analyze a multigrid method for a diffusion problem with jumping coefficients, and we analyze various block smoothers.

We show how to create a flexible software for the automation of local Fourier analysis. This flexibility is achieved by choosing approximations to Fourier matrix symbols as primitive components that are then combined into complicated expressions. In this way, many problems can be described and then analyzed by the software.

Bookmark:
Permalink | Share/Save
Dokumententyp:
Wissenschaftliche Abschlussarbeiten » Dissertation
Fakultäten und Einrichtungen:
Fakultät für Mathematik und Naturwissenschaften » Mathematik und Informatik » Dissertationen
Dewey Dezimal-Klassifikation:
500 Naturwissenschaften und Mathematik » 510 Mathematik » 518 Numerische Analysis
Keywords:
Multigrid, Fourier Analysis, Convergence Analysis, Stencils, Partial Differential Equations
Contributors:
Prof. Dr. Bolten, Matthias [Thesis advisor]
Prof. Dr. Bolten, Matthias [Reviewer]
Prof. Dr. Frommer, Andreas [Reviewer]
Prof. Dr. Jacob, Birgit [Reviewer]
Prof. Dr. MacLachlan, Scott [Reviewer]
Language:
Englisch
Collection / Status:
Dissertationen / Document published
Date of doctoral thesis submission:
19.06.2017
Files changed on:
22.01.2018
Date of doctoral degree:
20.10.2017
Medientyp:
Text
Rights remarks:
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ .