Partitioning techniques and their parallelization for stiff system of ordinary differential equations

A new code based on variable order and variable stepsize component wise partitioning is introduced to solve a system of equations dynamically. In previous partitioning technique researches, once an equation is identified as stiff, it will remain in stiff subsystem until the integration is complet...

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Main Author:	Othman, Khairil Iskandar
Format:	Thesis
Language:	English English
Published:	2007
Subjects:	Differential equations Stiff computation (Differential equations) Parallelizing compilers
Online Access:	http://psasir.upm.edu.my/id/eprint/8531/1/FS_2007_39_IR.pdf
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spelling	my-upm-ir.85312023-12-06T00:28:47Z Partitioning techniques and their parallelization for stiff system of ordinary differential equations 2007-04 Othman, Khairil Iskandar A new code based on variable order and variable stepsize component wise partitioning is introduced to solve a system of equations dynamically. In previous partitioning technique researches, once an equation is identified as stiff, it will remain in stiff subsystem until the integration is completed. In this current technique, the system is treated as nonstiff and any equation that caused stiffness will be treated as stiff equation. However, should the characteristics showed the elements of nonstiffness, and then it will be treated again with Adam method. This process will continue switching from stiff to nonstiff vice versa whenever it is necessary until the interval of integration is completed.Next, a block method with R-points generate R new approximate solution values;is a strategy for solving a system and also for parallelizing ODEs. Partitioning this block method to solve stiff differential equations is a new strategy; it is more efficient and takes less computational time compared to the sequential methods. Two partitioning techniques are constructed, Intervalwise Block Partitioning (IBP) and Componentwise Block Partitioning (CBP). Numerical results are compared as validation of its effectiveness. Intervalwise block partitioning will initially treat the systems of equations as nonstiff and solve them using Adams method, by switching to the Backward Differentiation formula when there is a step failure and indication of stiffness. Componentwise block partitioning will place the necessary equations that cause instability and stiffness into the stiff subsystem and solve using Backward Differentiation Formula, while all other equations will still be treated as non-stiff and solved using Adams formula. Parallelizing the partitioning strategies using Message Passing Interface (MPI) is the most appropriate method to solve large system of equations. Parallelizing the right algorithm in the partitioning code will give a better perfonnance with shorter execution times. The graphs of its performance and execution time, visualize the advantages of parallelizing. Differential equations Stiff computation (Differential equations) Parallelizing compilers 2007-04 Thesis http://psasir.upm.edu.my/id/eprint/8531/ http://psasir.upm.edu.my/id/eprint/8531/1/FS_2007_39_IR.pdf text en public doctoral Universiti Putra Malaysia Differential equations Stiff computation (Differential equations) Parallelizing compilers Faculty of Science Ismail, Fudziah English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
advisor	Ismail, Fudziah
topic	Differential equations Stiff computation (Differential equations) Parallelizing compilers
spellingShingle	Differential equations Stiff computation (Differential equations) Parallelizing compilers Othman, Khairil Iskandar Partitioning techniques and their parallelization for stiff system of ordinary differential equations
description	A new code based on variable order and variable stepsize component wise partitioning is introduced to solve a system of equations dynamically. In previous partitioning technique researches, once an equation is identified as stiff, it will remain in stiff subsystem until the integration is completed. In this current technique, the system is treated as nonstiff and any equation that caused stiffness will be treated as stiff equation. However, should the characteristics showed the elements of nonstiffness, and then it will be treated again with Adam method. This process will continue switching from stiff to nonstiff vice versa whenever it is necessary until the interval of integration is completed.Next, a block method with R-points generate R new approximate solution values;is a strategy for solving a system and also for parallelizing ODEs. Partitioning this block method to solve stiff differential equations is a new strategy; it is more efficient and takes less computational time compared to the sequential methods. Two partitioning techniques are constructed, Intervalwise Block Partitioning (IBP) and Componentwise Block Partitioning (CBP). Numerical results are compared as validation of its effectiveness. Intervalwise block partitioning will initially treat the systems of equations as nonstiff and solve them using Adams method, by switching to the Backward Differentiation formula when there is a step failure and indication of stiffness. Componentwise block partitioning will place the necessary equations that cause instability and stiffness into the stiff subsystem and solve using Backward Differentiation Formula, while all other equations will still be treated as non-stiff and solved using Adams formula. Parallelizing the partitioning strategies using Message Passing Interface (MPI) is the most appropriate method to solve large system of equations. Parallelizing the right algorithm in the partitioning code will give a better perfonnance with shorter execution times. The graphs of its performance and execution time, visualize the advantages of parallelizing.
format	Thesis
qualification_level	Doctorate
author	Othman, Khairil Iskandar
author_facet	Othman, Khairil Iskandar
author_sort	Othman, Khairil Iskandar
title	Partitioning techniques and their parallelization for stiff system of ordinary differential equations
title_short	Partitioning techniques and their parallelization for stiff system of ordinary differential equations
title_full	Partitioning techniques and their parallelization for stiff system of ordinary differential equations
title_fullStr	Partitioning techniques and their parallelization for stiff system of ordinary differential equations
title_full_unstemmed	Partitioning techniques and their parallelization for stiff system of ordinary differential equations
title_sort	partitioning techniques and their parallelization for stiff system of ordinary differential equations
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science
publishDate	2007
url	http://psasir.upm.edu.my/id/eprint/8531/1/FS_2007_39_IR.pdf
_version_	1794018763846189056

Partitioning techniques and their parallelization for stiff system of ordinary differential equations

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