Discrete random walk on large spherical grids generated by spherical means for PDEs*
-
K. K. Sabelfeld
, I. A. Shalimova and A. I. Levykin
A new general stochastic-deterministic approach for a numerical solution of boundary value problems of potential and elasticity theories is suggested. It is based on the use of the Poisson-like integral formulae for overlapping spheres. An equivalent system of integral equations is derived and then approximated by a system of linear algebraic equations. We develop two classes of special Monte Carlo iterative methods for solving these systems of equations which are a kind of stochastic versions of the Chebyshev iteration method and successive overrelaxation method (SOR). In the case of classical potential theory this approach accelerates the convergence of the well known Random Walk on Spheres method (RWS). What is however much more important, this approach suggests a first construction of a fast convergent finite-variance Monte Carlo method for the system of Lamé equations.
© de Gruyter 2004
Articles in the same Issue
- Foreword
- An outline of quasi-probability*: Why quasi-Monte-Carlo methods are statistically valid and how their errors can be estimated statistically
- QMC techniques for CAT bond pricing*
- Parallel Quasi-Monte Carlo Methods for Linear Algebra Problems
- Algorithm of statistical simulation of dynamic systems with distributed change of structure*
- Frequency Analysis of Semiconductor Devices Using Full-Band Cellular Monte Carlo Simulations
- The ⊝-Maruyama scheme for stochastic functional differential equations with distributed memory term*
- Subdiffusion and Superdiffusion in Lagrangian Stochastic Models of Oceanic Transport
- Approximations of functional integrals with respect to measures generated by solutions of stochastic differential equations
- Normalization of the Spectral Test in High Dimensions
- A spectral Monte Carlo method for the Poisson equation
- Convergence rate for spherical processes with shifted centres*
- On the Power of Quantum Algorithms for Vector Valued Mean Computation
- Parallel Quasirandom Walks on the Boundary
- Trajectory Splitting by Restricted Replication
- Upper Bounds for Bermudan Style Derivatives
- Stochastic Eulerian model for the flow simulation in porous media. Unconfined aquifers*
- Solution of the Space-dependent Wigner Equation Using a Particle Model
- Subgrid Modeling of Filtration in a Porous Medium with Multiscale Log-Stable permeability
- Comparison of Quasi-Monte Carlo-Based Methods for Simulation of Markov Chains
- Monte Carlo methods for fissured porous media: a gridless approach*
- Smoothed Transformed Density Rejection*
- Adaptive adjoint Monte Carlo simulation for the uncertainty
- A Nuclear Measurement Technique of Water Penetration in Concrete Barriers
- System availability and reliability analysis by direct Monte Carlo with biasing
- On the Scrambled Halton Sequence
- Monte-Carlo simulation of the chord length distribution function across convex bodies, non-convex bodies and random media
- Discrepancy of sequences generated by dynamical system
- Operator-Split Method for Variance Reduction in Stochastic Solutions of the Wigner Equation
- Two variants of a stochastic Euler method for homogeneous balance differential equations*
- Full band Monte Carlo simulation - beyond the semiclassical approach
- Coin Tossing Algorithms for Integral Equations and Tractability
- Optimal Korobov Coefficients for Good Lattice Points in Quasi Monte Carlo Algorithms
- A theoretical view on transforming low-discrepancy sequences from a cube to a simplex
- Weighted simulation of steady-state transport within the standard Monte Carlo paradigm
- Dynamic probabilistic method of numerical modeling of multidimensional hydrometeorological fields
- Quasirandom Sequences in Branching Random Walks*
- Discrete random walk on large spherical grids generated by spherical means for PDEs*
- Reusing paths in radiosity and global illumination
- Measures of Uniform Distribution in Wavelet Based Image Compression
- Random Walk Algorithms for Estimating Effective Properties of Digitized Porous Media*
- Security of Pseudo-random Generator and Monte Carlo Method
- Randomization of Quasi-Monte Carlo Methods for Error Estimation: Survey and Normal Approximation*
- Monte Carlo Simulation of Narrow-Width SOI Devices: Incorporation of the Short Range Coulomb Interaction
- Dagger-sampling variance reduction in Monte Carlo reliability analysis
Articles in the same Issue
- Foreword
- An outline of quasi-probability*: Why quasi-Monte-Carlo methods are statistically valid and how their errors can be estimated statistically
- QMC techniques for CAT bond pricing*
- Parallel Quasi-Monte Carlo Methods for Linear Algebra Problems
- Algorithm of statistical simulation of dynamic systems with distributed change of structure*
- Frequency Analysis of Semiconductor Devices Using Full-Band Cellular Monte Carlo Simulations
- The ⊝-Maruyama scheme for stochastic functional differential equations with distributed memory term*
- Subdiffusion and Superdiffusion in Lagrangian Stochastic Models of Oceanic Transport
- Approximations of functional integrals with respect to measures generated by solutions of stochastic differential equations
- Normalization of the Spectral Test in High Dimensions
- A spectral Monte Carlo method for the Poisson equation
- Convergence rate for spherical processes with shifted centres*
- On the Power of Quantum Algorithms for Vector Valued Mean Computation
- Parallel Quasirandom Walks on the Boundary
- Trajectory Splitting by Restricted Replication
- Upper Bounds for Bermudan Style Derivatives
- Stochastic Eulerian model for the flow simulation in porous media. Unconfined aquifers*
- Solution of the Space-dependent Wigner Equation Using a Particle Model
- Subgrid Modeling of Filtration in a Porous Medium with Multiscale Log-Stable permeability
- Comparison of Quasi-Monte Carlo-Based Methods for Simulation of Markov Chains
- Monte Carlo methods for fissured porous media: a gridless approach*
- Smoothed Transformed Density Rejection*
- Adaptive adjoint Monte Carlo simulation for the uncertainty
- A Nuclear Measurement Technique of Water Penetration in Concrete Barriers
- System availability and reliability analysis by direct Monte Carlo with biasing
- On the Scrambled Halton Sequence
- Monte-Carlo simulation of the chord length distribution function across convex bodies, non-convex bodies and random media
- Discrepancy of sequences generated by dynamical system
- Operator-Split Method for Variance Reduction in Stochastic Solutions of the Wigner Equation
- Two variants of a stochastic Euler method for homogeneous balance differential equations*
- Full band Monte Carlo simulation - beyond the semiclassical approach
- Coin Tossing Algorithms for Integral Equations and Tractability
- Optimal Korobov Coefficients for Good Lattice Points in Quasi Monte Carlo Algorithms
- A theoretical view on transforming low-discrepancy sequences from a cube to a simplex
- Weighted simulation of steady-state transport within the standard Monte Carlo paradigm
- Dynamic probabilistic method of numerical modeling of multidimensional hydrometeorological fields
- Quasirandom Sequences in Branching Random Walks*
- Discrete random walk on large spherical grids generated by spherical means for PDEs*
- Reusing paths in radiosity and global illumination
- Measures of Uniform Distribution in Wavelet Based Image Compression
- Random Walk Algorithms for Estimating Effective Properties of Digitized Porous Media*
- Security of Pseudo-random Generator and Monte Carlo Method
- Randomization of Quasi-Monte Carlo Methods for Error Estimation: Survey and Normal Approximation*
- Monte Carlo Simulation of Narrow-Width SOI Devices: Incorporation of the Short Range Coulomb Interaction
- Dagger-sampling variance reduction in Monte Carlo reliability analysis