Solution of three-dimensional problems of the theory of elasticity using the Monte Carlo method. (English. Russian original) Zbl 0705.73300
J. Appl. Math. Mech. 52, No. 2, 270-274 (1988); translation from Prikl. Mat. Mekh. 52, No. 2, 341-345 (1988).
Two versions of the Monte Carlo (MC) method for solving problems of the theory of elasticity are discussed. One uses the process of random walk over spheres to solve the Lamé equations, and the other represents the quantity sought in the form of multiple integrals (e.g. when solving the Cauchy problem for the wave equation of the theory of elasticity in an unbounded space).
MSC:
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 60G50 | Sums of independent random variables; random walks |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
Keywords:
random walk over spheres; Lamé equations; multiple integrals; Cauchy problem; wave equationReferences:
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