A random walk on rectangles algorithm

DOI10.1007/s11009-006-7292-3zbMath1104.60046OpenAlexW2019720802MaRDI QIDQ2433258

Antoine Lejay, Madalina Deaconu

Publication date: 27 October 2006

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-006-7292-3

zbMATH Keywords

Green functionsMonte Carlo methodLaplace operatorDirichlet-Neumann problemnumerical algorithmrandom walk on spheres/squares/rectangles

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Signal detection and filtering (aspects of stochastic processes) (60G35) Applications of stochastic analysis (to PDEs, etc.) (60H30) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (20)

Stochastic simulation algorithms for solving a nonlinear system of drift-diffusion-Poisson equations of semiconductors ⋮ A first-passage kinetic Monte Carlo method for reaction-drift-diffusion processes ⋮ Computing the principal eigenvalue of the Laplace operator by a stochastic method ⋮ 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 ⋮ Simulation of reflected Brownian motion on two dimensional wedges ⋮ Stochastic simulation algorithms for solving transient anisotropic diffusion-recombination equations and application to cathodoluminescence imaging ⋮ Simulating diffusion processes in discontinuous media: a numerical scheme with constant time steps ⋮ Simulating diffusions with piecewise constant coefficients using a kinetic approximation ⋮ Stochastic finite differences for elliptic diffusion equations in stratified domains ⋮ The walk on moving spheres: a new tool for simulating Brownian motion's exit time from a domain ⋮ Computing the principal eigenelements of some linear operators using a branching Monte Carlo method ⋮ Stopped diffusion processes: boundary corrections and overshoot ⋮ Stochastic algorithm for solving transient diffusion equations with a precise accounting of reflection boundary conditions on a substrate surface ⋮ Simulation of diffusions by means of importance sampling paradigm ⋮ A global random walk on grid algorithm for second order elliptic equations ⋮ A global random walk on grid algorithm for second order elliptic equations ⋮ An implementation of Milstein's method for general bounded diffusions ⋮ Random walk on rectangles and parallelepipeds algorithm for solving transient anisotropic drift-diffusion-reaction problems ⋮ An algorithm for probabilistic solution of parabolic PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Monte Carlo method for Poisson's equation
• An algorithm for random walks over small ellipsoids for solving the general Dirichlet problem
• Simulation of a space-time bounded diffusion
• The conditional probability density function for a reflected Brownian motion
• A Feynman-Kac path-integral implementation for Poisson's equation using an \(h\)-conditioned Green's function
• A Monte Carlo method without grid for a fractured porous domain model
• Some Continuous Monte Carlo Methods for the Dirichlet Problem
• Convergence rate for spherical processes with shifted centres *
• Discrete random walk on large spherical grids generated by spherical means for PDEs *
• Random Walk Algorithms for Estimating Effective Properties of Digitized Porous Media *
• Integral Formulation of the Boundary Value Problems and the Method of Random Walk on Spheres
• On the transition densities for reflected diffusions

This page was built for publication: A random walk on rectangles algorithm