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Mapping and evaluation of parallel solution for stiff Ordinary differential equations on heterogeneous architectures based on FPGAs

Grant number: 19/08153-7
Support type:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): September 15, 2019
Effective date (End): September 14, 2020
Field of knowledge:Physical Sciences and Mathematics - Computer Science - Computer Systems
Principal researcher:Eduardo Marques
Grantee:Carlos Alberto Oliveira de Souza Junior
Supervisor abroad: Joao Manuel Paiva Cardoso
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Research place: Universidade do Porto (UP), Portugal  
Associated to the scholarship:17/14268-6 - Mapping and evaluation of ordinary differential equations on heterogeneous architectures, BP.DR


Many engineering problems that rely on physical laws and relations can be modelled in the form of differential equations. Differential Equations, in general, are either ODEs or PDEs regarding the number of variables. In this thesis work, we are particularly interested in the acceleration of a chemical reaction simulation that relies on a system of stiff ODEs targeting heterogeneous computing systems. We intend to explore Field-Programmable Gate Arrays (FPGAs) and Graphics Processing Units (GPUs) with mixed precision. Our case study is CCATT-BRAMS since our current project is a continuation of the master's thesis research. During the previous project, we used the Rosenbrock method in CCATT-BRAMS, and we implemented the Jacobi algorithm to improve $Ax = b$ linear problem. This research intends to go further by implementing implicit methods for stiff ODEs in OpenCL. In our literature review, we have identified five base algorithms of interest when solving chemical reaction problems using ODEs, namely, Quasi-Steady-State-Approximation, Backward differentiation formulas, Runge-Kutta, Rosenbrock, and Waveform Relaxation. During BEPE project, we are going to use LARA and ANTAREX, both are domain specific languages, for precision tuning of the generated OpenCL kernels. These tools has shown some promising results regarding precision tuning and code refactoring.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
OLIVEIRA DE SOUZA JUNIOR, CARLOS ALBERTO; BISPO, JOAO; CARDOSO, JOAO M. P.; DINIZ, PEDRO C.; MARQUES, EDUARDO. Exploration of FPGA-Based Hardware Designs for QR Decomposition for Solving Stiff ODE Numerical Methods Using the HARP Hybrid Architecture. ELECTRONICS, v. 9, n. 5, . (13/07375-0, 19/08153-7, 17/14268-6)

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