**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30685

##### Solution of Two Dimensional Quasi-Harmonic Equations with CA Approach

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

**Abstract:**

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

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1328492

**References:**

[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.