Quasi-Monte Carlo approach to particle simulation of the heat equation

William J. Morokoff, Russel Caflisch

Research output: Contribution to journalArticle

Abstract

The convergence of the Monte Carlo method for numerical integration can often be improved by replacing random numbers with more uniformly distributed numbers known as quasi-random. In this paper the convergence of Monte Carlo particle simulation is studied when these quasi-random sequences are used. For the one-dimensional heat equation discretized in both space and time, convergence is proved for a quasi-random simulation using reordering of the particles according to their position. Experimental results are presented for the spatially continuous heat equation in one and two dimensions. The results indicate that a significant improvement in both magnitude of error and convergence rate can be achieved over standard Monte Carlo simulations for certain low-dimensional problems.

Original languageEnglish (US)
Pages (from-to)1558-1573
Number of pages16
JournalSIAM Journal on Numerical Analysis
Volume30
Issue number6
StatePublished - Dec 1993

Fingerprint

Quasi-Monte Carlo
Heat Equation
Convergence Time
Reordering
Random Sequence
Random number
Monte Carlo method
Numerical integration
One Dimension
Error Rate
Convergence Rate
Two Dimensions
Simulation
Monte Carlo methods
Monte Carlo Simulation
Experimental Results
Hot Temperature
Standards
Monte Carlo simulation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Quasi-Monte Carlo approach to particle simulation of the heat equation. / Morokoff, William J.; Caflisch, Russel.

In: SIAM Journal on Numerical Analysis, Vol. 30, No. 6, 12.1993, p. 1558-1573.

Research output: Contribution to journalArticle

Morokoff, William J. ; Caflisch, Russel. / Quasi-Monte Carlo approach to particle simulation of the heat equation. In: SIAM Journal on Numerical Analysis. 1993 ; Vol. 30, No. 6. pp. 1558-1573.
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