Year: 2023
Author: Jiang Yu Nguwi, Guillaume Penent, Nicolas Privault
Communications in Computational Physics, Vol. 34 (2023), Iss. 2 : pp. 261–289
Abstract
We present an algorithm for the numerical solution of systems of fully nonlinear PDEs using stochastic coded branching trees. This approach covers functional nonlinearities involving gradient terms of arbitrary orders, and it requires only a boundary condition over space at a given terminal time $T$ instead of Dirichlet or Neumann boundary conditions at all times as in standard solvers. Its implementation relies on Monte Carlo estimation, and uses neural networks that perform a meshfree functional estimation on a space-time domain. The algorithm is applied to the numerical solution of the Navier-Stokes equation and is benchmarked to other implementations in the cases of the Taylor-Green vortex and Arnold-Beltrami-Childress flow.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0140
Communications in Computational Physics, Vol. 34 (2023), Iss. 2 : pp. 261–289
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Fully nonlinear PDEs systems of PDEs Navier-Stokes equations Monte Carlo method deep neural network branching process random tree.
Author Details
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Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees
Nguwi, Jiang Yu
Privault, Nicolas
Japan Journal of Industrial and Applied Mathematics, Vol. 40 (2023), Iss. 3 P.1745
https://doi.org/10.1007/s13160-023-00611-9 [Citations: 0]