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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| Format: | Thesis |
| Language: | English English |
| Published: |
2007
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/8531/1/FS_2007_39_IR.pdf |
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| Summary: | 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. |
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