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Volume 12
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Article

GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations

by
Nicolás Murúa
1,
Aníbal Coronel
2,*,
Alex Tello
3,
Stefan Berres
4,5 and
Fernando Huancas
6
1
Departamento de Ciencias de la Computación y Tecnologías de la Información, Facultad de Ciencias Empresariales, Universidad del Bío-Bío, Campus Fernando May, Chillán 3780000, Chile
2
Departamento de Ciencias Básicas, Centro de Ciencias Exactas UBB (CCE-UBB), Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán 3780000, Chile
3
Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1270300, Chile
4
Núcleo de Investigación en Bioproductos y Materiales Avanzados (BioMA), Universidad Católica de Temuco, Temuco 4780002, Chile
5
Integrata-Stiftung für Humane Nutzung der Informationstechnologie, Vor dem Kreuzberg 28, 72070 Tübingen, Germany
6
Departamento de Matemática, Facultad de Ciencias Naturales, Matemáticas y del Medio Ambiente, Universidad Tecnológica Metropolitana, Las Palmeras 3360, Ñuñoa, Santiago 7750000, Chile
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(22), 3503; https://doi.org/10.3390/math12223503
Submission received: 3 October 2024 / Revised: 4 November 2024 / Accepted: 6 November 2024 / Published: 9 November 2024
(This article belongs to the Special Issue Advances in High-Performance Computing, Optimization and Simulation)
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Abstract

In this paper, we consider the finite difference approximation for a one-dimensional mathematical model of heat conduction in a three-layered solid with interfacial conditions for temperature and heat flux between the layers. The finite difference scheme is unconditionally stable, convergent, and equivalent to the solution of two linear algebraic systems. We evaluate various methods for solving the involved linear systems by analyzing direct and iterative solvers, including GPU-accelerated approaches using CuPy and PyCUDA. We evaluate performance and scalability and contribute to advancing computational techniques for modeling complex physical processes accurately and efficiently.
Keywords: sparse linear systems; finite difference method; heat transfer; GPU acceleration; high-performance computing; parallel processing; computational efficiency sparse linear systems; finite difference method; heat transfer; GPU acceleration; high-performance computing; parallel processing; computational efficiency

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MDPI and ACS Style

Murúa, N.; Coronel, A.; Tello, A.; Berres, S.; Huancas, F. GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations. Mathematics 2024, 12, 3503. https://doi.org/10.3390/math12223503

AMA Style

Murúa N, Coronel A, Tello A, Berres S, Huancas F. GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations. Mathematics. 2024; 12(22):3503. https://doi.org/10.3390/math12223503

Chicago/Turabian Style

Murúa, Nicolás, Aníbal Coronel, Alex Tello, Stefan Berres, and Fernando Huancas. 2024. "GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations" Mathematics 12, no. 22: 3503. https://doi.org/10.3390/math12223503

APA Style

Murúa, N., Coronel, A., Tello, A., Berres, S., & Huancas, F. (2024). GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations. Mathematics, 12(22), 3503. https://doi.org/10.3390/math12223503

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