2025
Topics in Numerical Analysis
Name: Topics in Numerical Analysis
Code: MAT11695D
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
It is intended that students acquire skills in the theoretical basis of different mathematical models
associated with fluid dynamics. On the theoretical / practical students will study and implement some of
the numerical mathematical models taught in the classroom using appropriate software.
associated with fluid dynamics. On the theoretical / practical students will study and implement some of
the numerical mathematical models taught in the classroom using appropriate software.
Contents
The course will be taught in modules. Students choose three of the following modules:
I. Numerical modeling of fluid dynamics: Mathematical models of Newtonian fluids and non-Newtonian and
analysis. Numerical methods. Applications in 1D, 2D and 3D.
II. Numerical modeling of turbulence: Introduction to turbulence, Kolmogorov cascade, power dissipation,
intermittency. Direct numerical simulation (DNS) of vertices and simulation (LES).
III. Computational meshes: meshes uniform and nonuniform. Computational mesh generation. Adaptive
meshes, structured and unstructured.
IV. Multiprocessing: Decomposition of domains. Parallelization of algorithms. Linear algebra algorithms
multiprocessor. Introduction to the implementation of finite element and finite differences for
multiprocessing.
V. Numerical methods for integral equations
I. Numerical modeling of fluid dynamics: Mathematical models of Newtonian fluids and non-Newtonian and
analysis. Numerical methods. Applications in 1D, 2D and 3D.
II. Numerical modeling of turbulence: Introduction to turbulence, Kolmogorov cascade, power dissipation,
intermittency. Direct numerical simulation (DNS) of vertices and simulation (LES).
III. Computational meshes: meshes uniform and nonuniform. Computational mesh generation. Adaptive
meshes, structured and unstructured.
IV. Multiprocessing: Decomposition of domains. Parallelization of algorithms. Linear algebra algorithms
multiprocessor. Introduction to the implementation of finite element and finite differences for
multiprocessing.
V. Numerical methods for integral equations
Teaching Methods
Exposure structured by examples, small project of investigation/demonstration to be undertaken by students. Inspection through 2 partial exames(and/or investigation project) or a final exame.
Teaching Staff
- Paulo Manuel de Barros Correia [responsible]
Certificações
