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A Spectral Deferred Correction Metho...

Bowen, Matthew M.

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A Spectral Deferred Correction Method for Solving Cardiac Models.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	A Spectral Deferred Correction Method for Solving Cardiac Models./
Author:	Bowen, Matthew M.
Description:	76 p.
Notes:	Source: Dissertation Abstracts International, Volume: 72-07, Section: B, page: .
Contained By:	Dissertation Abstracts International72-07B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3452927
ISBN:	9781124607535

A Spectral Deferred Correction Method for Solving Cardiac Models.
Bowen, Matthew M.

A Spectral Deferred Correction Method for Solving Cardiac Models. - 76 p.

Source: Dissertation Abstracts International, Volume: 72-07, Section: B, page: .

Thesis (Ph.D.)--Duke University, 2011.

Many numerical approaches exist to solving models of electrical activity in the heart. These models consist of a system of stiff nonlinear ordinary differential equations for the voltage and other variables governing channels, with the voltage coupled to a diffusion term. In this work, we propose a new algorithm that uses two common discretization methods, operator splitting and finite elements. Additionally, we incorporate a temporal integration process known as spectral deferred correction. Using these approaches, we construct a numerical method that can achieve arbitrarily high order in both space and time in order to resolve important features of the models, while gaining accuracy and efficiency over lower order schemes.

ISBN: 9781124607535Subjects--Topical Terms:

1669109
Applied Mathematics.

A Spectral Deferred Correction Method for Solving Cardiac Models.
LDR:02966nam 2200361 4500 001 1404929
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008 130515s2011 ||||||||||||||||| ||eng d
020 $a 9781124607535
035 $a (UMI)AAI3452927
035 $a AAI3452927
040 $a UMI $c UMI
100 1 $a Bowen, Matthew M. $3 1684277
245 1 2 $a A Spectral Deferred Correction Method for Solving Cardiac Models.
300 $a 76 p.
500 $a Source: Dissertation Abstracts International, Volume: 72-07, Section: B, page: .
500 $a Adviser: David G. Schaeffer.
502 $a Thesis (Ph.D.)--Duke University, 2011.
520 $a Many numerical approaches exist to solving models of electrical activity in the heart. These models consist of a system of stiff nonlinear ordinary differential equations for the voltage and other variables governing channels, with the voltage coupled to a diffusion term. In this work, we propose a new algorithm that uses two common discretization methods, operator splitting and finite elements. Additionally, we incorporate a temporal integration process known as spectral deferred correction. Using these approaches, we construct a numerical method that can achieve arbitrarily high order in both space and time in order to resolve important features of the models, while gaining accuracy and efficiency over lower order schemes.
520 $a Our algorithm employs an operator splitting technique, dividing the reaction-diffusion systems from the models into their constituent parts. We integrate both the reaction and diffusion pieces via an implicit Euler method. We reduce the temporal and splitting errors by using a spectral deferred correction method, raising the temporal order and accuracy of the scheme with each correction iteration.
520 $a Our algorithm also uses continuous piecewise polynomials of high order on rectangular elements as our finite element approximation. This approximation improves the spatial discretization error over the piecewise linear polynomials typically used, especially when the spatial mesh is refined.
520 $a As part of these thesis work, we also present numerical simulations using our algorithm of one of the cardiac models mentioned, the Two-Current Model. We demonstrate the efficiency, accuracy and convergence rates of our numerical scheme by using mesh refinement studies and comparison of accuracy versus computational time. We conclude with a discussion of how our algorithm can be applied to more realistic models of cardiac electrical activity.
590 $a School code: 0066.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Mathematics. $3 515831
650 4 $a Biophysics, General. $3 1019105
690 $a 0364
690 $a 0405
690 $a 0786
710 2 $a Duke University. $b Mathematics. $3 1036449
773 0 $t Dissertation Abstracts International $g 72-07B.
790 1 0 $a Schaeffer, David G., $e advisor
790 1 0 $a Trangenstein, John $e committee member
790 1 0 $a Layton, Anita T. $e committee member
790 1 0 $a Liu, Jian-Guo $e committee member
790 $a 0066
791 $a Ph.D.
792 $a 2011
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3452927