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An Accelerating Numerical Computation of the Diffusion Term in a Nonlocal Reaction-Diffusion Equation

Author

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  • Mitică CRAUS

    (Faculty of Automatic Control and Computer Engineering, Technical University “Gh. Asachi”, Dimitrie Mangeron, 27, 700050 Iaşi, Romania)

  • Silviu-Dumitru PAVĂL

    (Faculty of Automatic Control and Computer Engineering, Technical University “Gh. Asachi”, Dimitrie Mangeron, 27, 700050 Iaşi, Romania)

Abstract

In this paper we propose and compare two methods to optimize the numerical computations for the diffusion term in a nonlocal formulation for a reaction-diffusion equation. The diffusion term is particularly computationally intensive due to the integral formulation, and thus finding a better way of computing its numerical approximation could be of interest, given that the numerical analysis usually takes place on large input domains having more than one dimension. After introducing the general reaction-diffusion model, we discuss a numerical approximation scheme for the diffusion term, based on a finite difference method. In the next sections we propose two algorithms to solve the numerical approximation scheme, focusing on finding a way to improve the time performance. While the first algorithm (sequential) is used as a baseline for performance measurement, the second algorithm (parallel) is implemented using two different memory-sharing parallelization technologies: Open Multi-Processing (OpenMP) and CUDA. All the results were obtained by using the model in image processing applications such as image restoration and segmentation.

Suggested Citation

  • Mitică CRAUS & Silviu-Dumitru PAVĂL, 2020. "An Accelerating Numerical Computation of the Diffusion Term in a Nonlocal Reaction-Diffusion Equation," Mathematics, MDPI, vol. 8(12), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2111-:d:451332
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    References listed on IDEAS

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    1. Barbu, Tudor & Miranville, Alain & Moroşanu, Costică, 2019. "A qualitative analysis and numerical simulations of a nonlinear second-order anisotropic diffusion problem with non-homogeneous Cauchy–Neumann boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 170-180.
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