Keywords: high performance computing, interaction pantograph/catenary, dynamic equation, sparse linear algebra libraries.

Nowadays, society claims for better transport media, that mean, faster and more confortable. In a railway environment, faster transport can be seen as a problem of energy transmission. This energy transmission is produced in the interaction of the pantograph and catenary. An accurate model of this interaction becames essential due to the fact that a loss of contact between the pantograph and the catenary results in a loss of velocity. A very useful tool to study the behaviour of the model is the simulation by means of a set of algorithms. In this work, the calculation of the dynamical equation of the pantograph-catenary interaction in a stitched span is considered, not only from a mechanical point of view (an accurate model of the system), but also from the simulation point of view by means of a High Performance Computing Algorithm.

It is well known that in order to obtain an adequate behaviour in the pantograph/catenary system, it is necessary the existence of adequate conditions in the line, and this requires, among other aspects, a very precise mechanical calculus. Recent investigations have focused on dynamical behaviour by dynamical simulations in order to allow a better interaction of the pantograph and the catenary [4,2]; in this paper we will follow a more traditional approach, focusing in the catenary, modeled, as usual, by a set of coupled strings.

In this paper, a High Performance Computing Algorithm has been developed to obtain the solution of the dynamic problem of the pantograph/catenary system considering the stitched catenary which presents a better dynamical behaviour, because it maintains a more uniform stiffness along the span. Of course, the price to be paid consists on a greater complexity due to the existence of two kinds of carriers, the main and the secondary ones. Then, the amount of memory storage is considerable. So, it is necessary to deal with this kind of problem according to its sparse nature in order to reduce the memory requirements.

Sequential implementations of the resulting algorithm have been carried out by using standard libraries as BLAS [7] and SPARSKIT [8], in order to achieve good performance, portability, robutness and efficiency. In [] the HPC algorihms allow us to reduce the execution time. Lower memory requirements also allow us to deal with more realistic (bigger) problems and, of course, to better solve the dynamic problem, in particular with the stitched catenary. The experimental results show a spectacular reduction not only in memory storage requirements but also in execution time.

1

Poetsch G., J. Evans, R. Meisinger, W. Kortum, M. Baldauf, A. Veitl, & J. Wallaschek."Pantograph/catenary dynamics and control", Vehicle System Dynamics, 28:159-195, 1997. doi:10.1080/00423119708969353

2

Carsten, N.J. "Nonlinear systems with discrete and continuous elements", PhD thesis, University of, 1997.

3

Poetsch G., J. Wallaschek. "Symulating the dynamic behaviour of electrical lines for high-speed trains on parallel computers", International Symposium on Cable Dynamics, Liége, 1993.

4

Simeon, B., Arnold M. "The simulation of pantograph and catenary: a PDAE approach", Technical Report 1990, Fachbereich Mathematik Technische Universitat Darmstadt, 1998.

5

K.J. Bathe. "Finite Element Procedures in Engineering Analysis", Ed. Prentice-Hall, 1996.

6

Cook D.C., Malkus D.S., Plesha M.E. "Concepts and Applications of Finite Element Analysis", Ed. John Wiley and Sons, 1989.

7

J.J. Dongarra, J. Du Croz, I.S. Duff, S. Hammarling. "A set of Level 3 Basic Linear Algebra Subprograms", ACM Trans. Math. Soft, 1990. doi:10.1145/77626.79170

8

Y. Saad. "SPARSKIT: a basic tool kit for sparse matrix computations", University of Illinois and NASA Ames Research Center, 1994.

9

J. Benet, F. Cuartero, T. Rojo. "A tool to calculate catenaries in railways", Seventh International Conference on Computer in Railways, COMPRAIL-2000, 2000.

10

L. Argandoña, E. Arias, J. Benet, F. Cuartero, T. Rojo. "High performance computing in high speed railways", The Ninth International Conference on Civil and Structural Engineering Computing Civil-Comp 2003, Egmond aan Zee, The Netherlands, 2-4 September 2003, Civil-Comp Press, Stirling, UK. doi:10.4203/ccp.77.94

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