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Computing reachable sets via barrier methods on SIMD architectures

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 10-14, 2012 (e-book). - Vienna, Austria : Vienna University of Technology , 2012 . - pp. 2076-2095
ISBN 9783950248197

This is the latest version of this item.

Abstract in another language

We consider the problem of computing reachable sets of ODE-based 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 Runge-Kutta 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; Runge-Kutta 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.uni-bayreuth.de/id/eprint/9544

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