Monte Carlo solution of the finite-difference Dirichlet problem for the multidimensional Helmholtz equation
type: Item
instance of: scholarly article
title: Monte Carlo solution of the finite-difference Dirichlet problem for the multidimensional Helmholtz equation
zbMATH Open document ID: 0951.65002
author: A. F. Cheshkova
author: G. A. Mikhaĭlov
published in: Computational Mathematics and Mathematical Physics
publication date: 2000-07-02T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1467857
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Monte Carlo method
zbMATH Keywords: computational costs
zbMATH Keywords: finite-difference approximation
zbMATH Keywords: convergence
zbMATH Keywords: Neumann series
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1467857