Applying Rosenbrock method for solving stiff ODEs raised from the chemical reactivity of the atmosphere through heterogeneous architectures based on FPGAs

Author(s)

Carlos Alberto Oliveira de Souza Junior

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2023-04-03

Examining board members

Eduardo Marques; João Manuel Paiva Cardoso; Ricardo dos Santos Ferreira; Haroldo Fraga de Campos Velho

• Advisor: Eduardo Marques; Pedro Nuno Cruz Diniz

Abstract

This work focuses on the solution of Stiff Ordinary Differential Equations through numerical methods applied to hardware/software codesign techniques. Previous studies reveal that such problems require implicit methods to avoid the very small timesteps of explicit methods. The problem is that implicit methods are based on the conversion from non-linear systems to a system of linear equations, which requires linear systems of the form Ax = b. During the authors masters thesis, it became clear that CCATT-BRAMS linear systems require direct methods. In CCATT-BRAMS, that is solved by Rosenbrock Method that includes 4 computational stages (only the first stage requires a matrix decomposition). In that manner, it is possible to reuse previous decompositions for the algorithms subsequent stages to solve the ordinary differential equations. For that, we had to split Rosenbrock into two main tasks. The first relates to solving linear systems with direct methods and then modifying Rosenbrock to leverage the FPGA architecture. Our systematic review showed that very few works in the literature explore the parallelism of the stiff ordinary differential equations in chemical reactivity for FPGAs. In this thesis, we provide FPGA solutions based on Intel OpenCL HLS. Our results show that the generated hardware architecture is competitive and can improve the performance and power efficiency of such a critical application responsible for weather forecasting in Brazil. (AU)

• FAPESP's process: 17/14268-6 - Mapping and evaluation of ordinary differential equations on heterogeneous architectures
• Grantee: Carlos Alberto Oliveira de Souza Junior
• Support Opportunities: Scholarships in Brazil - Doctorate