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Accelerated Numerical Simulations of a Reaction-Diffusion- Advection Model Using Julia-CUDA

Author

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  • Angelo Ciaramella

    (Department of Science and Technology, Parthenope University of Naples, Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
    These authors contributed equally to this work.)

  • Davide De Angelis

    (Department of Science and Technology, Parthenope University of Naples, Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
    These authors contributed equally to this work.)

  • Pasquale De Luca

    (Department of Science and Technology, Parthenope University of Naples, Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
    International PhD Programme/UNESCO Chair “Environment, Resources and Sustainable Development”, Department of Science and Technology, Parthenope University of Naples, Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
    These authors contributed equally to this work.)

  • Livia Marcellino

    (Department of Science and Technology, Parthenope University of Naples, Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
    International PhD Programme/UNESCO Chair “Environment, Resources and Sustainable Development”, Department of Science and Technology, Parthenope University of Naples, Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
    These authors contributed equally to this work.)

Abstract

The emergence of exascale computing systems presents both opportunities and challenges in scientific computing, particularly for complex mathematical models requiring high-performance implementations. This paper addresses these challenges in the context of biomedical applications, specifically focusing on tumor angiogenesis modeling. We present a parallel implementation for solving a system of partial differential equations that describe the dynamics of tumor-induced blood vessel formation. Our approach leverages the Julia programming language and its CUDA capabilities, combining a high-level paradigm with efficient GPU acceleration. The implementation incorporates advanced optimization strategies for memory management and kernel organization, demonstrating significant performance improvements for large-scale simulations while maintaining numerical accuracy. Experimental results confirm the performance gains and reliability of the proposed parallel implementation.

Suggested Citation

  • Angelo Ciaramella & Davide De Angelis & Pasquale De Luca & Livia Marcellino, 2025. "Accelerated Numerical Simulations of a Reaction-Diffusion- Advection Model Using Julia-CUDA," Mathematics, MDPI, vol. 13(9), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1488-:d:1646956
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