Random Walk on Fixed Spheres for Laplace and Lamé equations

DOI10.1515/156939606776886634zbMath1122.65007OpenAlexW2030760966MaRDI QIDQ3412511

Alexander I. Levykin, Irina A. Shalimova, K. K. Sabel'fel'd

Publication date: 6 December 2006

Published in: Monte Carlo Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/156939606776886634

zbMATH Keywords

numerical experimentsLamé equationLaplace equationrandom walksystem of integral equationsPoisson integral formulaChebyshev iteration methodsuccessive over relaxation methodMonte Carlo iterative methods

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Sums of independent random variables; random walks (60G50) Classical linear elasticity (74B05) Numerical analysis or methods applied to Markov chains (65C40) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

Expansion of random boundary excitations for elliptic PDEs, Stochastic Algorithms in Linear Algebra - beyond the Markov Chains and von Neumann - Ulam Scheme, On solving stochastic differential equations, Sparsified Randomization Algorithms for large systems of linear equations and a new version of the Random Walk on Boundary method

Cites Work

• Optimal \(p\)-cyclic SOR
• Probabilistic approach to the Lamé equations of linear elastostatics.
• The method of finite spheres
• The local boundary integral equation (LBIE) and its meshless implementation for linear elasticity
• Discrete random walk on large spherical grids generated by spherical means for PDEs *
• A Poisson Integral Formula for the Ellipse and Some Applications
• The successive over relaxation method (SOR) and Markov chains
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