Title data
Grüne, Lars ; Jahn, Thomas U.:
Computing reachable sets via barrier methods on SIMD architectures.
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
.  pp. 20762095
ISBN 9783950248197
This is the latest version of this item.
Related URLs
Abstract in another language
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 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:  Article in a book 

Refereed:  Yes 
Additional notes:  Contents:
1. Introduction 2. Principles of SIMD architectures 2.1 SIMD and thread enumeration 2.2 Memory considerations 2.3 Suitable algorithms 3. Algorithm Specification 3.1 The approach of Baier and Gerdts 3.2 An algorithm for computing reachable sets 3.3 Distributing the algorithm to the CUDA hardware 4. Solving the feasibility problem 4.1 The interior–point algorithm 4.2 Defining the restrictions 4.3 Exploiting sparsity 5. Numerical examples 5.1 Rayleigh 5.2 Kenderov 6. Conclusions 
Keywords:  reachable set; feasibility problem; sparse linear equation system; RungeKutta method; CUDA; parallelization; lower arrow form 
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) 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  01 Apr 2015 06:32 
Last Modified:  01 Oct 2018 10:16 
URI:  https://eref.unibayreuth.de/id/eprint/9544 
Available Versions of this Item

Computing reachable sets via barrier methods on SIMD architectures. (deposited 28 Mar 2015 22:00)
 Computing reachable sets via barrier methods on SIMD architectures. (deposited 01 Apr 2015 06:32) [Currently Displayed]