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Stochastic diffusion processes on Cartesian meshes.

Lina Meinecke1, Per Lötstedt1

  • 1Division of Scientific Computing, Department of Information Technology Uppsala University, P. O. Box 337, SE-75105 Uppsala, Sweden.

Journal of Computational and Applied Mathematics
|November 24, 2015
PubMed
Summary

This study compares four methods for simulating molecular diffusion. Finite difference and finite volume methods provide the most accurate diffusion coefficients for stochastic simulations.

Keywords:
65C0565C3592C05Cartesian meshdiffusionstochastic simulation

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Area of Science:

  • Computational physics and chemistry
  • Numerical methods for diffusion simulation

Background:

  • Stochastic simulation of molecular diffusion is crucial in various scientific fields.
  • Accurate derivation of diffusion coefficients (propensities) is essential for reliable simulations.

Purpose of the Study:

  • To compare four distinct methods for calculating diffusion propensities in a Cartesian mesh.
  • To evaluate the accuracy and advantages of each method in stochastic diffusion simulations.

Main Methods:

  • Stochastic simulation of molecular diffusion using voxel jumps.
  • Derivation of jump coefficients via finite difference, finite element, and finite volume approximations.
  • Utilizing first exit time of a random walk in a voxel as an alternative coefficient derivation.

Main Results:

  • Finite difference and finite volume approximations yield the most accurate diffusion coefficients.
  • The first exit time method offers non-negative coefficients, an advantage for certain models.
  • Numerical experiments validate theoretical comparisons of the four methods.

Conclusions:

  • Finite difference and finite volume methods are recommended for accurate stochastic diffusion simulations.
  • The choice of method depends on the specific requirements for coefficient properties (e.g., non-negativity).
  • This work provides a framework for selecting appropriate numerical techniques for diffusion modeling.