Efficient probabilistic Poisson solver for complex geometries based on sparse markov matrices
Por:
Ramírez-Cabrera M.A., Ramos E., Valadés-Pelayo P.J.
Publicada:
1 ene 2024
Resumen:
This article introduces an efficient stochastic method to approximate the solution to Poisson’s Equation (PE). The method starts by computing sparse Transition Probability Matrices (TPMs), assembled by averaging short continuous random walks based on the transient diffusion equation with a source. The TPMs can be used within a false-transient approach to approximate the solution to PE in the steady-state limit. The method’s efficiency and memory usage are comparable to the Finite-Volume method. However, the ease of implementation, stability, and versatility makes the method attractive in complex scenarios. Moreover, given that the code can be easily implemented in parallel, it displays superior efficiency and practical importance in scenarios where a large number of nodes is mandatory. © 2023 Taylor & Francis Group, LLC.
Filiaciones:
Ramírez-Cabrera M.A.:
Ingeniería Eléctrica, Tecnológico Nacional de México/Instituto Tecnológico Superior de Huauchinango, Puebla, Huauchinango, Mexico
Ramos E.:
Instituto de Energías Renovables, Universidad Nacional Autónoma de México, Morelos, Temixco, Mexico
Valadés-Pelayo P.J.:
Instituto de Energías Renovables, Universidad Nacional Autónoma de México, Morelos, Temixco, Mexico
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