Next Article in Journal
Arcs, Caps and Generalisations in a Finite Projective Space
Previous Article in Journal
Exceptional Differential Polynomial Systems Formed by Simple Pseudo-Wronskians of Jacobi Polynomials and Their Infinite and Finite X-Orthogonal Reductions
Previous Article in Special Issue
New Strategies Based on Hierarchical Matrices for Matrix Polynomial Evaluation in Exascale Computing Era
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Mathematics
Volume 13
Issue 9
10.3390/math13091488
mathematics-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

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

by
Angelo Ciaramella
1,†,
Davide De Angelis
1,†,
Pasquale De Luca
1,2,*,† and
Livia Marcellino
1,2,†
1
Department of Science and Technology, Parthenope University of Naples, Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
2
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
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2025, 13(9), 1488; https://doi.org/10.3390/math13091488
Submission received: 7 April 2025 / Revised: 27 April 2025 / Accepted: 28 April 2025 / Published: 30 April 2025
(This article belongs to the Special Issue Advances in Numerical Mathematics for High-Performance Computing in the Exascale Era)
Versions Notes

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 parallel algorithm; GPU programming; Julia programming; tumor angiogenesis; numerical models

Share and Cite

MDPI and ACS Style

Ciaramella, A.; De Angelis, D.; De Luca, P.; Marcellino, L. Accelerated Numerical Simulations of a Reaction-Diffusion- Advection Model Using Julia-CUDA. Mathematics 2025, 13, 1488. https://doi.org/10.3390/math13091488

AMA Style

Ciaramella A, De Angelis D, De Luca P, Marcellino L. Accelerated Numerical Simulations of a Reaction-Diffusion- Advection Model Using Julia-CUDA. Mathematics. 2025; 13(9):1488. https://doi.org/10.3390/math13091488

Chicago/Turabian Style

Ciaramella, Angelo, Davide De Angelis, Pasquale De Luca, and Livia Marcellino. 2025. "Accelerated Numerical Simulations of a Reaction-Diffusion- Advection Model Using Julia-CUDA" Mathematics 13, no. 9: 1488. https://doi.org/10.3390/math13091488

APA Style

Ciaramella, A., De Angelis, D., De Luca, P., & Marcellino, L. (2025). Accelerated Numerical Simulations of a Reaction-Diffusion- Advection Model Using Julia-CUDA. Mathematics, 13(9), 1488. https://doi.org/10.3390/math13091488

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop