Automating finite difference codes with Devito to solve problems modeled by partial differential equations

• Grant number: 24/03241-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2024
• End date: April 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Gilcilene Sanchez de Paulo
• Grantee: Gabriel de Oliveira Portes
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

In this project, we aim to investigate how Devito can accelerate the development process of a finite difference code, improve computational efficiency, and facilitate the exploration of complex problems in various application areas, such as computational fluid dynamics (CFD), for example. This project will provide practical insight into the use of Devito as a simple and effective tool to automate the implementation of finite difference codes, enhance computational efficiency, and facilitate the exploration of complex problems in various application areas. Consequently, it is expected that a student in a Bachelor's degree program in Mathematics can develop the minimum skills necessary for this area by paying attention to the details of developing an accurate numerical methodology from a mathematical perspective. The Devito platform will be applied to solve prototypes of parabolic, hyperbolic, and elliptic partial differential equations (PDEs), as well as mixed problems, in order to confront theoretical studies with numerical results. General and specific aspects of each discretization will be extensively discussed, such as concepts of convergence, stability, consistency, employment of boundary conditions, interpretation and presentation of results, verification (accuracy and robustness) of the methodologies employed. Additionally, the aim is to discuss the advantages and challenges associated with using Devito to deal with more complex, multidimensional, and nonlinear problems so that the applicability of this platform can be expanded by the group.