Efficient Simulation of Physical System Models Using Inlined Implicit Runge-Kutta Algorithms

Vicha Treeaporn
Department of Electrical and Computer Engineering
The University of Arizona
Tucson, Arizona 85721
U.S.A.
Email: VichaT@U.Arizona.Edu

Abstract

Stiff systems commonly occur in science and engineering, and the use of an implicit integration algorithm is typically needed to simulate them. As model complexity increases, the need for efficient ways to solve these types of systems is becoming of increasing importance. Using a technique called inline–integration with implicit Runge–Kutta (IRK) algorithms and tearing may lead to a more efficient simulation. To further increase the efficiency of the simulation, the step–size of the integration algorithm can be controlled. By using larger integration steps when allowable, the simulation can progress with fewer computations while still maintaining the desired accuracy.

In this thesis, for the purpose of step–size control, two new embedding methods will be proposed. The first will be for HW-SDIRK(3)4, a singly diagonally implicit Runge–Kutta (SDIRK) algorithm and the second for Lobatto IIIC(6). These two embedding methods will then be compared with those previously found for the Radau IIA family and Lobatto IIIC(4), all fully–implicit Runge–Kutta algorithms.

Interested in reading the entire thesis? (118 pages, 1,506,190 bytes, pdf)
Interested in viewing the Powerpoint presentation?

Homepage