Monte Carlo solution of the finite-difference Dirichlet problem for the multidimensional Helmholtz equation
The authors analyze the computational costs of both direct and conjugate Monte Carlo solutions of the set of algebraic equations that correspond to the conventional finite-difference approximation of the Dirichlet problem for the multidimensional Helmholtz differential equation. The convergence of the Neumann series is proved and an approximate optimum relation between the mesh and sample sizes is obtained.
scientific article; zbMATH DE number 1467857