Monte Carlo Methods in Boundary Value Problems
This book deals with Random Walk Methods for solving multidimensional boundary value problems. Monte Carlo algorithms are constructed for three classes of problems: (1) potential theory, (2) elasticity, and (3) diffusion. Some of the advantages of our new methods as compared to conventional numerical methods are that they cater for stochasticities in the boundary value problems and complicated shapes of the boundaries.
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Monte Carlo Algorithms for Solving Integral Equations
Monte Carlo Algorithms for Solving Boundary
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adjoint aerosol aerosol particles analytical continuation approximation arbitrary assume atoms Au(x boundary algorithm boundary dG boundary integral equations boundary process boundary value problem capture coefficient Chap circle constant construct continued fraction converges curve defined denote derivatives diffusion Dirichlet problem domain G double randomization e-biased e-spherical process example exterior finite fixed gaussian Green's function homogeneous random field inequality inside the domain island isotropic iterations kernel Lagrangian Laplace linear Markov chain matrix mean value relation Monte Carlo estimate Monte Carlo methods Neumann problem Neumann series Note number of steps obtain parameter potential theory radius random estimate random number random point random variables random vector right-hand side sampled satisfies seek the solution simulation formulas spectral tensor spheres algorithm spheres process statistical characteristics subdomains Theorem theory trajectories transformation transition density turbulent unbiased estimate variance velocity field walk on boundary walk on spheres Wiener process