Abstract
The classic way to describe electrostatic field is using Partial Differential Equations and suitable boundary conditions. In most situations we need numerical methods mainly based on discretisation of time and space. In this paper we follow a different approach: we introduce RNR Cellular Automata that is capable of modeling the electrostatic field at macroscopic level. Iterations of the automata are averaged on time and space to get continuous variables. We implement RNR Cellular Automata with FPGA and compare the performance with the results using classic sequential programming. We get some regular architectures specially adapted to fully-parallel machines, and explore its benefits and drawbacks.
Candidate to the best student paper award.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Wolfram, S.: Statistical mechanics of cellular automata. Reviews of Modern Physics 55, 601–644 (1983)
Toffoli, T.: Occam, Turing, von Neumann, Jaynes: How much can you get for how little? (A conceptual introduction to cellular automata). The Interjournal (October 1994)
Wolfram, S.: A New Kind of Science. Wolfram media, Champaign (2002)
Margolus, N.: Physics-Like models of computation. Physica 10D, 81–95 (1984)
Toffoli, T.: Cellular Automata as an alternative to (rather than an approximation of) Differential Equations in Modeling Physics. Physica 10D, 117–127 (1984)
Smith, M.A.: Cellular Automata Methods in Mathematical Physics. Ph.D. Thesis. MIT Department of Physics (May 1994)
Sarkar, P.: A brief history of cellular automata. ACM Computing Surveys 32(1), 80–107 (2000)
Shackleford, B., Tanaka, M., Carter, R.J., Snider, G.: FPGA Implementation of Neighborhood-of-Four Cellular Automata Random Number Generators. In: Proceedings of FPGA 2002, pp. 106–112 (2002)
Levich, B.G.: Curso de Física teórica. Volumen I: Teoría del campo electromagnético y teoría de la relatividad. Reverté (1974)
Gerald, C.F., Wheatley, P.O.: Applied Numerical Analysis, 6th edn. Addison Wesley Longman, Amsterdam (1999)
Cerdá-Boluda, J.: Arquitecturas VLSI de Autómatas Celulares para Modelado Físico. Ph.D Thesis. UPV Electronic Engineering Dept. (to be published)
Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press, Cambridge (1999)
Marsaglia, G.: DIEHARD (1996), http://stat.fsu.edu/~geo/diehard.html
Jaquenod, G., De Giusti, M.R.: Performance y uso de recursos de contadores basados en Linear Feedback Shift Registers (LFSRs). In: VIII Workshop IBERCHIP, Guadalajara, México (2002)
Chew, W.C., Jin, J.M., Lu, C.C., Michielssen, E., Song, J.M.: Fast Solution Methods in Electromagnetics. IEEE Transactions on Antennas and Propagation 45(3), 523–533 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cerdá-Boluda, J., Amoraga-Lechiguero, O., Torres-Curado, R., Gadea-Gironés, R., Sebastià-Cortés, A. (2005). FPGA Implementations of the RNR Cellular Automata to Model Electrostatic Field . In: Daydé, M., Dongarra, J., Hernández, V., Palma, J.M.L.M. (eds) High Performance Computing for Computational Science - VECPAR 2004. VECPAR 2004. Lecture Notes in Computer Science, vol 3402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11403937_30
Download citation
DOI: https://doi.org/10.1007/11403937_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25424-9
Online ISBN: 978-3-540-31854-5
eBook Packages: Computer ScienceComputer Science (R0)