By Topic

Fast parallel recursive aggregation methods for simulation of dynamical systems

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
W. K. Tsai ; Dept. of Electr. & Comput. Eng., California Univ., Irvine, CA, USA ; Garng Huang ; Wei Lu

A novel recursive aggregation algorithm for numerical simulations of dynamic systems is proposed and analyzed. The algorithm exploits a special structure of the linear equation problem resulting from the discretization of the dynamic system and an aggregation/disaggregation procedure. The algorithm has a time complexity of (I(q)+2M(q)+3)logN for solving linear systems with q states for N discrete time instants, using O(q3N) processors, where I(q) is the parallel time complexity for inverting a q×q matrix, M(q) is the parallel time complexity for matrix multiplication of two q×q matrices. The competing parallel cyclic reduction method for the same problem has a time complexity of (I(q)+3M(q)+4)logN. Thus, the proposed algorithm has a definite speed advantage over the cyclic reduction method. An approximation technique for the unknown boundary conditions in boundary value problems is also proposed. The algorithm was implemented to simulate some dynamical (stable and unstable) systems, and the numerical results show that the accumulation of roundoff errors is insignificant as compared to the discretization errors

Published in:

IEEE Transactions on Automatic Control  (Volume:39 ,  Issue: 3 )