The ``walk in hemispheres process and its applications to solving boundary value problems

DOI10.3103/S1063454109030029zbMath1181.65009MaRDI QIDQ1036939

Alexander Sipin, Sergeĭ Mikhaĭlovich Ermakov

Publication date: 13 November 2009

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemboundary value problem on polytopewalk in hemispheres process

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Sums of independent random variables; random walks (60G50) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Numerical analysis or methods applied to Markov chains (65C40) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (9)

Random walk on spheres algorithm for solving transient drift-diffusion-reaction problems ⋮ A global random walk on spheres algorithm for transient heat equation and some extensions ⋮ Stochastic and quasistochastic computations ⋮ Stochastic algorithm for solving transient diffusion equations with a precise accounting of reflection boundary conditions on a substrate surface ⋮ A global random walk on grid algorithm for second order elliptic equations ⋮ A global random walk on grid algorithm for second order elliptic equations ⋮ Random walk on rectangles and parallelepipeds algorithm for solving transient anisotropic drift-diffusion-reaction problems ⋮ Monte Carlo Method for Partial Differential Equations ⋮ Stochastic algorithms for solving the Dirichlet boundary value problem for certain second-order elliptic equations with discontinuous coefficients

Cites Work

• Monte Carlo methods for solving elliptic equations with boundary conditions containing the normal derivative
• Some Continuous Monte Carlo Methods for the Dirichlet Problem
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