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

Angelo Ciaramella, Davide De Angelis, Pasquale De Luca () and Livia Marcellino
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Angelo Ciaramella: Department of Science and Technology, Parthenope University of Naples, Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
Davide De Angelis: Department of Science and Technology, Parthenope University of Naples, Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
Pasquale De Luca: Department of Science and Technology, Parthenope University of Naples, Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
Livia Marcellino: Department of Science and Technology, Parthenope University of Naples, Naples, Centro Direzionale Isola C4, 80143 Naples, Italy

Mathematics, 2025, vol. 13, issue 9, 1-21

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.

Keywords: parallel algorithm; GPU programming; Julia programming; tumor angiogenesis; numerical models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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