TECHNICAL PAPERS: Conduction Heat Transfer

A Monte Carlo Solution of Heat Conduction and Poisson Equations

[+] Author and Article Information
M. Grigoriu

Cornell University, Ithaca, NY 14853-3501e-mail: mdg12@cornell.edu

J. Heat Transfer 122(1), 40-45 (Aug 31, 1999) (6 pages) doi:10.1115/1.521435 History: Received June 09, 1997; Revised August 31, 1999
Copyright © 2000 by ASME
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Emery,  A. F., and Carson,  W. W., 1968, “A Modification to the Monte Carlo Method—The Exodus Method,” ASME J. Heat Transfer, 90, pp. 328–332.
Haji-Sheikh,  A., and Sparrow,  E. M., 1967, “The Solution of Heat Conduction Problems by Probability Methods,” ASME J. Heat Transfer, 89, pp. 121–130.
Klahr, C. N., 1960, “A Monte Carlo Method for the Solution of Elliptic Partial Differential Equation,” Mathematical Methods for Digital Computers, A. Ralston and H. S. Wilf, eds., John Wiley and Sons, New York, pp. 157–164.
Sadiku,  M. N. O., and Hunt,  D. T., 1992, “Solution of Dirichlet problems by Exodus Methods,” IEEE Trans. Microwave Theory Tech., 40, No. 1, pp. 89–95.
Sadiku,  M. N. O., Ajose,  S. O., and Fu,  Z., 1994, “Applying the Exodus Methods to Solve Poisson’s Equation,” IEEE Trans. Microwave Theory Tech., 42, No. 4, pp. 661–666.
Zinsmeister,  G. E., and Sawyerr,  J. A., 1974, “A Method for Improving the Efficiency of Monte Carlo Calculations of Heat Conduction Problems,” ASME J. Heat Transfer, 96, pp. 246–248.
Suresh, K., 1966, “Fast Point Solution Techniques in Engineering Analysis,” Advances in Mechanical Engineering, T. S. Mruthyunjava, ed., Narosa Publishing House, New Delhi, India, pp. 385–400.
Zagajac, J., 1995, “A Fast Method for Estimating Discrete Field Values in Early Engineering Design,” Proceedings of the Third Symposium on Solid Modeling and Applications, C. Hoffmann and J. Rossignac, eds., Salt Lake City, UT, May, pp. 420–430.
Courant, R., and Hilbert, D., 1966, Methods of Mathematical Physics, Vol. 2, John Wiley and Sons, New York.
Grigoriu,  M., 1997, “Local Solutions of Laplace, Heat, and Other Equations by Ito⁁ Processes,” ASCE J. Eng. Mech., 123, No. 8, pp. 823–829.
Muller,  M. E., 1956, “Some Continuous Monte Carlo Methods for the Dirichlet Problem,” Ann. Math. Stat., 27, No. 3, pp. 569–589.
Chung, K. L., and Williams, R. J., 1990, Introduction to Stochastic Integration, 2nd Ed., Birkhäuser, Boston.
Grigoriu, M., 1995, Applied Non-Gaussian Process: Examples, Theory, Simulation, Linear Random Vibration, and MATLAB Solutions, Prentice-Hall, Englewood Cliffs, NJ.
O̸ksendal, B., 1992, Stochastic Differential Equations, 3rd Ed., Springer-Verlag, New York.
Kloeden, P. E., and Platen, E., 1980, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, New York.
Greenberg, M. D., 1978, Foundations of Applied Mathematics, Prentice-Hall, Englewood Cliffs, NJ.





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