Parallel linear solver performance analysis

• Grant number: 19/08632-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2019
• End date: May 31, 2020
• Field of knowledge: Engineering - Mechanical Engineering - Transport Phenomena
• Principal Investigator: Leandro Franco de Souza
• Grantee: Victor Augusto de Oliveira Coelho
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

This project aims to analyze codes that solve linear systems parallel to solve the Poisson equation. The most efficient algorithms will be used, in a second step, in a parallel numerical solution code of the Navier-Stokes equations for incompressible flow of Newtonian fluid. The key point of the numerical solution of the Navier-Stokes equations for incompressible flows is the numerical solution of the Poisson equation. The supervisor of this work has already worked with the a parallel study of this equation in one and two directions, and in this project it is sought to verify and compare the performance of the code developed by the group with the available PETSC (Portable Extensible Toolkit for Scientific Computation) package. The results obtained from the solutions of the partial differential equations will be compared with the results where the analytical solution is known, in order to verify the accuracy of the implemented methods. The results of the parallel Navier-Stokes code for the simulation of incompressible flows will be compared with other results for verification of the final code. It is also intended to verify the performance and speed of the code, comparing the total time spent in the sequential case (a single processor) and in the parallel case (two or more processors).