A Global Random Walk on Spheres algorithm for calculating the solution and its derivatives of the drift-diffusion-reaction equations

Karl Sabelfeld, Anastasya Kireeva

Research output: Contribution to journalArticlepeer-review

Abstract

A Global Random Walk on Spheres (GRWS) algorithm for calculating the solution and its derivatives of drift-diffusion-reaction equations in any desired set of points is suggested. The GRWS algorithm is able to find the solution and derivative fields in any family of points simultaneously, using only one ensemble of random walks which drastically decreases the computer time compared to the standard random walk-based methods. The method in its nature is stochastic and meshless; the cost is of the order (Formula presented.) independent of the space dimension and complexity of the boundary shape, where ε is the desired accuracy. The variance, accuracy, and the cost of the method suggested are given. For illustration, we present simulation results for exciton drift-diffusion-recombination transport in a 3D prism and compare them with the exact solution. Calculations are also given for derivatives of a 2D diffusion problem which show the same accuracy as for the solution itself; the simulations are compared against the exact results.

Original languageEnglish
JournalMathematical Methods in the Applied Sciences
Early online date7 Oct 2021
DOIs
Publication statusE-pub ahead of print - 7 Oct 2021

Keywords

  • adjoint Green function
  • drift-diffusion-Poisson equation
  • fundamental solution
  • Global Random Walk algorithm
  • Random Walk on Spheres

OECD FOS+WOS

  • 1.01 MATHEMATICS

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