Sequential and Localized Implicit Wavelet Based Solvers for Stiff Partial Differential Equations

Sequential and Localized Implicit Wavelet Based Solvers for Stiff Partial Differential Equations

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This thesis explains and tests a wavelet based implicit numerical method for the solving of partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time discr...

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Main Author: McLaren, Donald Alexander
Language:en
Published: 2012
Subjects:
wavelet
implicit
multi-scale
pde
Online Access:http://hdl.handle.net/10393/22822
id ndltd-LACETR-oai-collectionscanada.gc.ca-OOU-OLD.-22822
record_format oai_dc
spelling ndltd-LACETR-oai-collectionscanada.gc.ca-OOU-OLD.-228222013-04-05T03:21:09ZSequential and Localized Implicit Wavelet Based Solvers for Stiff Partial Differential EquationsMcLaren, Donald Alexanderwaveletimplicitmulti-scalepdeThis thesis explains and tests a wavelet based implicit numerical method for the solving of partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time discretization into multiple, smaller, systems that can be solved sequentially. Included are tests of this method on linear and non-linear problems, with both its results and the time required to calculate them compared to basic models. It was found that the method requires less computational effort than the high resolution control results. Furthermore, the method showed convergence towards high resolution control results.2012-05-01T16:11:09Z2012-05-01T16:11:09Z20122012-05-01Thèse / Thesishttp://hdl.handle.net/10393/22822en
collection NDLTD
language en
sources NDLTD
topic wavelet
implicit
multi-scale
pde
spellingShingle wavelet
implicit
multi-scale
pde
McLaren, Donald Alexander
Sequential and Localized Implicit Wavelet Based Solvers for Stiff Partial Differential Equations
description This thesis explains and tests a wavelet based implicit numerical method for the solving of partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time discretization into multiple, smaller, systems that can be solved sequentially. Included are tests of this method on linear and non-linear problems, with both its results and the time required to calculate them compared to basic models. It was found that the method requires less computational effort than the high resolution control results. Furthermore, the method showed convergence towards high resolution control results.
author McLaren, Donald Alexander
author_facet McLaren, Donald Alexander
author_sort McLaren, Donald Alexander
title Sequential and Localized Implicit Wavelet Based Solvers for Stiff Partial Differential Equations
title_short Sequential and Localized Implicit Wavelet Based Solvers for Stiff Partial Differential Equations
title_full Sequential and Localized Implicit Wavelet Based Solvers for Stiff Partial Differential Equations
title_fullStr Sequential and Localized Implicit Wavelet Based Solvers for Stiff Partial Differential Equations
title_full_unstemmed Sequential and Localized Implicit Wavelet Based Solvers for Stiff Partial Differential Equations
title_sort sequential and localized implicit wavelet based solvers for stiff partial differential equations
publishDate 2012
url http://hdl.handle.net/10393/22822
work_keys_str_mv AT mclarendonaldalexander sequentialandlocalizedimplicitwaveletbasedsolversforstiffpartialdifferentialequations
_version_ 1716579561292955648

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