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TECHNICAL PAPERS

Local Solutions in Potential Theory and Linear Elasticity Using Monte Carlo Methods

[+] Author and Article Information
S. S. Kulkarni, S. Mukherjee

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853

M. D. Grigoriu

Department of Environmental and Civil Engineering, Cornell University, Ithaca, NY 14853e-mail: mdg12@cornell.edu

J. Appl. Mech 70(3), 408-417 (Jun 11, 2003) (10 pages) doi:10.1115/1.1558074 History: Received November 30, 2001; Revised August 20, 2002; Online June 11, 2003
Copyright © 2003 by ASME
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References

Arsenjev, D. G., Ivanov, V. M., and Kul’chitsky, O. Y., 1999, Adaptive Methods of Computational Mathematics and Mechanics, Stochastic Varient, World Scientific, Singapore.
Kim,  C. I., and Torquato,  S., 1989, “Determination of the Effective Conductivity of Heterogeneous Media by Brownian Motion Simulation,” J. Appl. Phys., 68, 3892–3903.
Evans, M., and Swartz, T., 2000, Approximating Integrals via Monte Carlo and Deterministic Methods, Oxford University Press, Oxford, UK.
Sabelfeld, K. K., 1991, Monte Carlo Methods in Boundary Value Problems, Springer-Verlag, Berlin.
Sabelfeld, K. K., and Simonov, N. A., 1994, Random Walks on Boundary for Solving PDEs, VSP, Utrecht, The Netherlands.
Hoffman,  T. J., and Banks,  N. E., 1974, “Monte Carlo Solution to the Dirichlet Problem With the Double Layer Potential Density,” Trans. Am. Nucl. Soc., 18, pp. 136–137.
Kalos, H. K., and Whitlock, A. P., 1986, Monte Carlo Methods, John Wiley and Sons, New York.
Haj-Sheikh,  A., and Sparrow,  E. M., 1966, “The Floating Random Walk and Its Applications to Monte Carlo Solutions of Heat Transfer,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 14, pp. 370–389.
Sabelfeld,  K. K., and Talay,  D., 1995, “Integral Formulation of the Boundary Value Problems and the Method of the Random Walk on the Spheres,” Monte Carlo Meth. Appl.,1, pp. 1–34.
Chati,  K. C., Grigoriu,  M. D., Kulkarni,  S. S., and Mukherjee,  Subrata, 2001, “Random Walk Method for the Two- and Three-dimensional Laplace, Poisson and Helmholt’z Equations,” Int. J. Numer. Methods Eng., 51 , pp. 1133–1156.
O̸ksendal, B., 1992, Stochastic Differential Equations, Springer, New York.
Kupradze, V. D., 1965, Potential Methods in the Theory of Elasticity, Israel Program for Scientific Translations, Jerusalem.
Mikhailov,  S. E., 1989, “Spectral Properties and Solution Methods for Some Integral Equations of Elasticity for Plane Non-Simply-Connected Bodies with Corner Points Under Forces Specified on the Boundary,” Mech. Solids, 24, pp. 53–63.
Shia,  D., and Hui,  C., 2000, “A Monte Carlo Solution Method for Linear Elasticity,” Int. J. Solids Struct., 37, pp. 6085–6105.
Rubinstein, R. Y., 1981, Simulation and the Monte Carlo Method, John Wiley and Sons, New York.
Jaswon, M. A., and Symm, G. T., 1977, Integral Equation Methods in Potential Theory and Elastostatics, Academic Press, New York.
Günter, N. M., 1967, Potential Theory, Frederick Ungar, New York.
Rizzo,  F. J., 1967, “An Integral Equation Approach to Boundary Value Problems of Classical Elastostatics,” Q. J. Mech. Appl. Math., 25, pp. 83–95.
Parton, V. Z., and Perlin, P. I., 1982, Integral Equations in Elasticity, Mir, Moscow.
Atkinson, K. E., 1997, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge, UK.
Wasow,  W., 1957, “Asymptotic Development of the Solution of Dirichlet’s Problem at Analytic Corner,” Duke Math. J., 24, pp. 47–56.

Figures

Grahic Jump Location
Intermediate distribution
Grahic Jump Location
Pie-shaped region for the Dirichlet problem
Grahic Jump Location
Wedge-shaped region for the displacement problem
Grahic Jump Location
Problem definition for the traction prescribed problem

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