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Random walk algorithms for solving nonlinear chemotaxis problems. / Sabelfeld, Karl K.; Bukhasheev, Oleg.

In: Monte Carlo Methods and Applications, Vol. 30, No. 3, 03.08.2024, p. 235-248.

Research output: Contribution to journal › Article › peer-review

Harvard

Sabelfeld, KK & Bukhasheev, O 2024, 'Random walk algorithms for solving nonlinear chemotaxis problems', Monte Carlo Methods and Applications, vol. 30, no. 3, pp. 235-248. https://doi.org/10.1515/mcma-2024-2008

APA

Sabelfeld, K. K., & Bukhasheev, O. (2024). Random walk algorithms for solving nonlinear chemotaxis problems. Monte Carlo Methods and Applications, 30(3), 235-248. https://doi.org/10.1515/mcma-2024-2008

Vancouver

Sabelfeld KK, Bukhasheev O. Random walk algorithms for solving nonlinear chemotaxis problems. Monte Carlo Methods and Applications. 2024 Aug 3;30(3):235-248. doi: 10.1515/mcma-2024-2008

Author

Sabelfeld, Karl K. ; Bukhasheev, Oleg. / Random walk algorithms for solving nonlinear chemotaxis problems. In: Monte Carlo Methods and Applications. 2024 ; Vol. 30, No. 3. pp. 235-248.

BibTeX

@article{0b6488daddb347ba8427ec7dca619467,
title = "Random walk algorithms for solving nonlinear chemotaxis problems",
abstract = "Random walk based stochastic simulation methods for solving a nonlinear system of coupled transient diffusion and drift-diffusion equations governing a two-component chemotaxis process are developed. The nonlinear system is solved by linearization, the system is evolved in time, by small time steps, where on each step a linear system of equations is solved by using the solution from the previous time step. Three different stochastic algorithms are suggested, (1) the global random walk on grid (GRWG), (2) a randomized vector algorithm (RVA) based on a special transformation of the original matrix to a stochastic matrix, and (3) a stochastic projection algorithm (SPA). To get high precision results, these methods are combined with an iterative refinement method. ",
keywords = "Chemotaxis process, Keller–Segel equation, global random walk on grid, randomized vector linear solver, stochastic projection method",
author = "Sabelfeld, {Karl K.} and Oleg Bukhasheev",
year = "2024",
month = aug,
day = "3",
doi = "10.1515/mcma-2024-2008",
language = "English",
volume = "30",
pages = "235--248",
journal = "Monte Carlo Methods and Applications",
issn = "0929-9629",
publisher = "Walter de Gruyter GmbH",
number = "3",

}

RIS

TY - JOUR

T1 - Random walk algorithms for solving nonlinear chemotaxis problems

AU - Sabelfeld, Karl K.

AU - Bukhasheev, Oleg

PY - 2024/8/3

Y1 - 2024/8/3

N2 - Random walk based stochastic simulation methods for solving a nonlinear system of coupled transient diffusion and drift-diffusion equations governing a two-component chemotaxis process are developed. The nonlinear system is solved by linearization, the system is evolved in time, by small time steps, where on each step a linear system of equations is solved by using the solution from the previous time step. Three different stochastic algorithms are suggested, (1) the global random walk on grid (GRWG), (2) a randomized vector algorithm (RVA) based on a special transformation of the original matrix to a stochastic matrix, and (3) a stochastic projection algorithm (SPA). To get high precision results, these methods are combined with an iterative refinement method.

AB - Random walk based stochastic simulation methods for solving a nonlinear system of coupled transient diffusion and drift-diffusion equations governing a two-component chemotaxis process are developed. The nonlinear system is solved by linearization, the system is evolved in time, by small time steps, where on each step a linear system of equations is solved by using the solution from the previous time step. Three different stochastic algorithms are suggested, (1) the global random walk on grid (GRWG), (2) a randomized vector algorithm (RVA) based on a special transformation of the original matrix to a stochastic matrix, and (3) a stochastic projection algorithm (SPA). To get high precision results, these methods are combined with an iterative refinement method.

KW - Chemotaxis process

KW - Keller–Segel equation

KW - global random walk on grid

KW - randomized vector linear solver

KW - stochastic projection method

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85200321019&origin=inward&txGid=429bf044df98d2c1beb2d619f7948c9

UR - https://www.mendeley.com/catalogue/b67f3e9f-271d-3af3-a918-888154098954/

U2 - 10.1515/mcma-2024-2008

DO - 10.1515/mcma-2024-2008

M3 - Article

VL - 30

SP - 235

EP - 248

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

SN - 0929-9629

IS - 3

ER -

ID: 60848767