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Parallel Programming in Finite Difference Method to Solve Turing's Model of Spot Pattern

Published: 27 February 2023 Publication History

Abstract

Turing's model is a model contains reaction-diffusion equation that capable to form skin patterns on an animal. In this paper, Turing's model was investigated, with the model improvisation by Barrio et al. [12], in parallel programming to shown its speed up impact. The parallel programming managed to speed up the process up to 8.9 times while retaining the quality of the result, compared to traditional programming.

References

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A. M. Turing. 1952. The Chemical Basis of Morphogenesis. Philos. Trans. R. Soc. Lond, Ser. B. Biol. Vol. 237, No. 641 (Aug. 1952), 37-72. https://doi.org/10.1098/rstb.1952.0012
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L. M. McNamara. 2017. Comprehensive Biomaterials II, 2.10 Bone as a Material, 202-227. Elsevier. https://doi.org/10.1016/B978-0-12-803581-8.10127-4
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T. Sekimura, A. Madzvamuse, A. J. Wathen, and P. K. Maini, 2000. A model for colour pattern formation in the butterfly wing of Papilio Dardanus. In Proceedings of the Royal Society B Biological Sciences, 7 May, 2000, London, Royal Society. https://doi.org/10.1098/rspb.2000.1081
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F. Shakeri and M. Dehghan. 2011. The finite volume spectral element method to solve Turing models in the biological pattern formation. Comput. Math. With Appl. 62, 12 (Dec. 2011), 4322-4336 https://doi.org/10.1016/j.camwa.2011.09.049
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A. Madzvamuse, A. J. Wathen, P. K. Maini, 2003. A moving grid finite element method applied to a model biological pattern generator. J. Comput. Phys. 190, 2 (Sept. 2003), 478-500. https://doi.org/10.1016/S0021-9991(03)00294-8
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J. Zhu, Y. -T. Zhang, S. A. Newman, M. Alber, 2009. Application of discontinuous Galerkin methods for reaction-diffusion systems in developmental biology. J. Sci, Comput. 40, (July 2009), 391-418. https://doi.org/10.1007/s10915-008-9218-4
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R. T. Liu, S. S. Liaw, and P. K. Maini, 2005. Two-stage Turing model for generating pigment patterns on the leopard and the jaguar. Phys. Rev. E 74, 1, 011914 (July 2006). https://doi.org/10.1103/PhysRevE.74.011914
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J. H. E. Cartwright. 2001. Labyrinthine Turing Pattern Formation in the Cerebral Cortex. J. Theor. Biol. 217, 1 (March 2002), 97-103. https://doi.org/10.1006/jtbi.2002.3012
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H. Kim, A. Yun, S. Yoon, C. Lee, J. Park, J. Kim, 2020. Pattern formation in reaction-diffusion systems on evolving surfaces. Comput. Math. With Appl. 80, 9 (Nov. 2020), 2019-2028. https://doi.org/10.1016/j.camwa.2020.08.026
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S. A. Sarra. 2012. A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains. App. Math. And Comp. 218 (2012), 9853-9865. https://doi.org/10.1016/j.amc.2012.03.062
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M. W. Smiley. 2008. An efficient implementation of a numerical method for a chemotaxis system. J. Comput. Math. 86, 2 (Dec. 2008), 219-235. https://doi.org/10.1080/00207160701864475
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R. A. Barrio, C. Varea, J. L. Aragon, 1999. A Two-dimensional Numerical Study of Spatial Pattern Formation in Interacting Turing Systems. Bull. Math. Biol. 61, (May 1999), 483-505. https://doi.org/10.1006/bulm.1998.0093
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W. L. Allen, I. C. Cuthill, N. E. Scott-Samuel, R. Baddeley, 2010. Why the leopard got its spot: relating pattern development to ecology in felids. In Proceedings of the Royal Society B Biological Sciences, 20 Oct. 2010, London, Royal Society. https://doi.org/10.1098/rspb.2010.1734
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J. C. Butcher. 2008. Numerical Methods for Ordinary Differential Equations (2nd. Ed.). John Wiley & Sons, Chichester, West Sussex, UK.
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A. H. Workie. 2020. New Modification on Heun's Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency. J. Math. 2020, Article 6650855 (Dec. 2020). https://doi.org/10.1155/2020/6650855
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J. Cheng, M. Grossman, T. McKercher, 2014. Professional CUDA C Programming. John Wiley & Sons, Indianapolis, Indiana, US.

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IC3INA '22: Proceedings of the 2022 International Conference on Computer, Control, Informatics and Its Applications
November 2022
415 pages
ISBN:9781450397902
DOI:10.1145/3575882
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 27 February 2023

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  1. Heun's method
  2. Turing's model
  3. finite difference
  4. parallel programming

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