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B-spline adaptive collocation/Runge-Kutta software with interpolation-based spatial error estimation for the error-controlled numerical solution of PDEs Muir, Paul
Description
An essential component of a high quality numerical software package is a framework that provides an error-controlled computation of the approximate solution. This means that the package returns a numerical solution such that an associated error estimate satisfies a user-prescribed tolerance. This type of computation has two important advantages: (i) the user can have reasonable confidence that the numerical solution has an error that is consistent with the requested tolerance, and (ii) the cost of the computation will be consistent with the requested accuracy. In this talk, we introduce a new software package, called BACOLRI, for the error-controlled numerical solution of 1D PDEs. This code employs a high order B-spline collocation algorithm to discretize the spatial domain and then uses a high order error control Runge-Kutta package to solve the resulting system of time-dependent Differential-Algebraic Equations. BACOLRI estimates the spatial error of the approximate solution on each time-step using an interpolation-based scheme and employs adaptive mesh refinement to provide control of the spatial error. We will briefly survey the family of solvers from which BACOLRI has evolved, describe the algorithms implemented in BACOLRI, and review numerical results that demonstrate the superior performance of BACOLRI compared to other comparable solvers.
Item Metadata
Title |
B-spline adaptive collocation/Runge-Kutta software with interpolation-based spatial error estimation for the error-controlled numerical solution of PDEs
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-05-31T15:28
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Description |
An essential component of a high quality numerical software package is a framework that provides an error-controlled computation of the approximate solution. This means that the package returns a numerical solution such that an associated error estimate satisfies a user-prescribed tolerance. This type of computation has two important advantages: (i) the user can have reasonable confidence that the numerical solution has an error that is consistent with the requested tolerance, and (ii) the cost of the computation will be consistent with the requested accuracy.
In this talk, we introduce a new software package, called BACOLRI, for the error-controlled numerical solution of 1D PDEs. This code employs a high order B-spline collocation algorithm to discretize the spatial domain and then uses a high order error control Runge-Kutta package to solve the resulting system of time-dependent Differential-Algebraic Equations. BACOLRI estimates the spatial error of the approximate solution on each time-step using an interpolation-based scheme and employs adaptive mesh refinement to provide control of the spatial error. We will briefly survey the family of solvers from which BACOLRI has evolved, describe the algorithms implemented in BACOLRI, and review numerical results that demonstrate the superior performance of BACOLRI compared to other comparable solvers.
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Extent |
33.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Saint Mary's University
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Series | |
Date Available |
2019-03-25
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0377452
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International