Commenced in January 2007
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Solution of Two Dimensional Quasi-Harmonic Equations with CA Approach

Authors: F. Rezaie Moghaddam, J. Amani, T. Rezaie Moghaddam


Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.

Keywords: cellular automata, Heat Conduction, discrete system, convergencerate

Digital Object Identifier (DOI):

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[1] H. Arzani and M. H. Afshar, "Solving Poisson-s equations by the discrete least square meshless method." WIT Transactions on Modeling and Simulation, 2006, 42: p.p.23-31.
[2] A. R. Firoozjaee and M. H. Afshar "Collocation discrete least square meshless method for the solution of free surface problem." International Journal of Civil Engineering, 2007, 5(2): p.p.134-143.
[3] S. Ulam, "A collection of mathematical problems--, Inter science Publishers, New York, 1960.
[4] S. Ulam, "Adventures of a mathematician--, Charles Scribner's Sons, New York, 1983.
[5] S. Ulam, "Random processes and transformations--, In Proceeding of International Congress of Mathematics 2, pp 85-87, April 1952.
[6] J. Von Neumann, "Theory of self-reproducing automata--, Univ. of Illinois Press, Champaign, IL, 1966.
[7] S. Wolfram, "A New Kind of Science--, Wolfram Media, Inc., Champaign, IL, USA, 2002.
[8] S. Wolfram, "Cellular automata as models of complexity--, 1984, Nature, 31 (4), pp 419-424.
[9] S. Wolfram, "Statistical mechanics of cellular automata--, Rev. Mod. Phys. 55, 601, 1983.
[10] S. Wolfram, "Theory and application of cellular automata--, World Scientific, Singapore, 1984.
[11] S. Wolfram, "Cellular automata and complexity: collected papers--, Addison-Wisely Publishing Company, 1994.
[12] B. Chopard and M. Droz, "Cellular Automata Modeling of Physical Systems--, Collection Alea-Sacley, Cambridge University Press, Cambridge, UK, 1998.
[13] T. Toffoli, "Cellular Automata as an Alternative to (rather than approximation of) Differential Equations in Modeling Physics--, Physica D, 10, 1984, pp 117-127.
[14] J. Weimar, "Simulation with Cellular Automata--, Logos-Verlag, Berlin, 1998.
[15] Z. G├╝rdel and B. Tatting, "Cellular automata for design of truss structures with linear and nonlinear response--, 41th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference & Exhibit, Atlanta, Georgia, April 2000.
[16] S. Missoum, Z. G├╝rdel and W. Gu, "Optimization of nonlinear trusses using a displacement based approach--, Struct. Multidisc. Optim. 23, pp 214-221, 2000.
[17] S. Missoum, M. Abdalla and Z. G├╝rdel, "Nonlinear topology design of trusses using cellular automata--, 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Norfolk, Virginia 2003.
[18] H. Cortés, A. Tovar, J.D. Mu├▒oz, N.M. Patel and J.E. Renaud, "Topology optimization of truss structures using cellular automata with accelerated simultaneous analysis and design--, 6th World Congresses of structural and multidisciplinary optimization. Reo de Janeiro, Brazil 2005.
[19] A. Tovar, N.M. Patel, A.K. Kaushik and J.E. Renaud, "Optimality conditions of the hybrid cellular automata for structural optimization--, AIAA Journal, 2007, 45 (3), pp 673-683.
[20] S. Setoodeh, Z. G├╝rdal and L. T. Watson, "Design of variable-stiffness composite layers using cellular automata", Computer Methods in Applied Mechanics and Engineering 195 (9-12), 2006, pp 836-851.
[21] S. Setoodeh, M. M. Abdalla, and Z. G├╝rdal, "Combined topology and fiber path design of composite layers using cellular automata", Structural and Multidisciplinary Optimization, 30 (6), 2005, pp 413-421.
[22] S. Setoodeh, D. B. Adams, Z. G├╝rdal and L. T. Watson, "Pipeline implementation of cellular automata for structural design on messagepassing multiprocessors", Mathematical and Computer Modeling, 43, 2006, pp 966-975.
[23] E. F. Moore, "Machine models of self-reproducing--, Proc. Symp. Appl. Math. 14, 17, 1962.