Análise e Geração de Resultados sobre Implementação de Método Runge-Kutta em CUDA
Resumo
O presente trabalho compreende a análise e avaliação de implementações do método Runge-Kutta em interface de programação paralela CUDA. Foram testadas 3 implementações de segunda e quarta ordem do método. Como resultados, foram feitas medições de performance e qualidade das soluções numéricas das implementações encontradas na literatura.
Referências
Butcher, J. (2016). Numerical Methods for Ordinary Differential Equations. Wiley.
Butcher, J. C. (1987). The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods. Wiley-Interscience.
Chatterjee, B. C. B. . D. (2011). Numerical Method and Programming (WBUT), 2nd Edition. Vikas Publishing House.
Dorodnitsyn, A. (1953). Asymptotic Solution of Van Der Pol’s Equation. American Mathematical Society translations. American Mathematical Society.
Novotny, J., Green, M., and Boston, R. (2012). Mathematical Modeling in Nutrition and the Health Sciences. Advances in Experimental Medicine and Biology. Springer US.
Sparrow, C. (2012). The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Applied Mathematical Sciences. Springer New York.
Wo, M. S., Gobithaasan, R., and Miura, K. (2013). GPU Acceleration of Runge Kutta-Fehlberg and Its Comparison with Dormand-Prince Method. volume 1605.
Butcher, J. C. (1987). The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods. Wiley-Interscience.
Chatterjee, B. C. B. . D. (2011). Numerical Method and Programming (WBUT), 2nd Edition. Vikas Publishing House.
Dorodnitsyn, A. (1953). Asymptotic Solution of Van Der Pol’s Equation. American Mathematical Society translations. American Mathematical Society.
Novotny, J., Green, M., and Boston, R. (2012). Mathematical Modeling in Nutrition and the Health Sciences. Advances in Experimental Medicine and Biology. Springer US.
Sparrow, C. (2012). The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Applied Mathematical Sciences. Springer New York.
Wo, M. S., Gobithaasan, R., and Miura, K. (2013). GPU Acceleration of Runge Kutta-Fehlberg and Its Comparison with Dormand-Prince Method. volume 1605.
Publicado
18/04/2022
Como Citar
MOREIRA, Nórton Lopes; SCHEPKE, Claudio; CABRAL, Axel Manuel da Silva.
Análise e Geração de Resultados sobre Implementação de Método Runge-Kutta em CUDA. In: ESCOLA REGIONAL DE ALTO DESEMPENHO DA REGIÃO SUL (ERAD-RS), 22. , 2022, Curitiba.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2022
.
p. 17-20.
ISSN 2595-4164.
DOI: https://doi.org/10.5753/eradrs.2022.19150.
