Title data
Grüne, Lars ; Jahn, Thomas U.:
Computing reachable sets via barrier methods on SIMD architectures.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2012
.  20 S.


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Abstract
We consider the problem of computing reachable sets of ODEbased control systems parallely on CUDA hardware. To this end, we modify an existing algorithm based on solving optimal control problems. The idea is to simplify the optimal control problems to pure feasibility problems instead of minimizing an objective function. We show that an interior point algorithm is well suited for solving the resulting feasibility problems and leads to a sequence of linear systems of equations with identical matrix layout. If the problem is defined properly, these matrices are sparse and can be transformed into a hierarchical lower arrow form which can be solved on CUDA hardware with sparse linear algebra and Cholesky’s method. We demonstrate the performance of our new algorithm by computing the reachable sets of two test problems on a CPU implementation using several explicit and implicit RungeKutta methods of different order. The experiments reveal a significant speedup compared to the original optimal control algorithm.
Further data
Item Type:  Preprint, postprint 

Additional notes (visible to public):  erscheint in:
Eberhardsteiner, Josef ; Böhm, Helmut J. ; Rammerstorfer, Franz G. (eds.): Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) Held at the University of Vienna, Austria, September 1014, 2012 (ebook).  Vienna, Austria : Vienna University of Technology , 2012 .  S. 20762095 ISBN 9783950248197 
Keywords:  reachable set; feasibility problem; sparse linear equation system; RungeKutta method; CUDA; parallelization; lower arrow form 
DDC Subjects:  500 Science > 510 Mathematics 
Institutions of the University:  Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics)  Univ.Prof. Dr. Lars Grüne Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) 
Language:  English 
Originates at UBT:  Yes 
URN:  urn:nbn:de:bvb:703epub19646 
Date Deposited:  27 Mar 2015 10:11 
Last Modified:  02 Jun 2021 10:09 
URI:  https://epub.unibayreuth.de/id/eprint/1964 