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

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.