2024
Computational Mechanics and Optimization
Name: Computational Mechanics and Optimization
Code: EME13149M
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mechanical Engineering
Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
Knowledge of available tools for Computational Mechanics.
Knowledge of Computational Linear Algebra, root finding, ODE and PDE and graph visualization.
To provide state-of-the-art information concerning Computational Mechanics and Optimization, to promote analytical reasoning and the capability to perform numerical implementations.
Specifically, students should be able to work with algorithms so that convergence rates, error analysis and heuristics are considered.
Ability to formalize problems in applied subjects such as aerospace structures and optimization of productive processes.
Knowledge of Computational Linear Algebra, root finding, ODE and PDE and graph visualization.
To provide state-of-the-art information concerning Computational Mechanics and Optimization, to promote analytical reasoning and the capability to perform numerical implementations.
Specifically, students should be able to work with algorithms so that convergence rates, error analysis and heuristics are considered.
Ability to formalize problems in applied subjects such as aerospace structures and optimization of productive processes.
Contents
1. Polynomial interpolation.
2. Numerical quadrature: basic methods and Gauss methods.
3. Brief introduction to dense linear algebra. BLAS operations.
4. Nonlinear equations making use of first derivatives.
5. Brent method and combination with Newton method. Functions that change sign and industrial-strength root finders.
6. ODE integration.
7. Sparse eigenvalue problems.
8. Introduction to partial differential equations (PDE). Finite difference methods for PDE. Galerkin method and finite element method.
9. Unconstrained optimization. Optimality conditions of first and second orders. Conjugate gradient method, Newton method and Quasi-Newton families.
10. Trust region method with dogleg.
11. Equality-constrained problems. Constraint classification. Transformation methods.
12. Inequality-constrained problems. Complementarity.
13. Numerical solution of PDE problems: Fourier heat equations and Cauchy equilibrium.
14. Applications to structural optimization
2. Numerical quadrature: basic methods and Gauss methods.
3. Brief introduction to dense linear algebra. BLAS operations.
4. Nonlinear equations making use of first derivatives.
5. Brent method and combination with Newton method. Functions that change sign and industrial-strength root finders.
6. ODE integration.
7. Sparse eigenvalue problems.
8. Introduction to partial differential equations (PDE). Finite difference methods for PDE. Galerkin method and finite element method.
9. Unconstrained optimization. Optimality conditions of first and second orders. Conjugate gradient method, Newton method and Quasi-Newton families.
10. Trust region method with dogleg.
11. Equality-constrained problems. Constraint classification. Transformation methods.
12. Inequality-constrained problems. Complementarity.
13. Numerical solution of PDE problems: Fourier heat equations and Cauchy equilibrium.
14. Applications to structural optimization
Teaching Methods
The methodologies correspond to the traditional in this theme, but with the advantage of having equipment and experience in the areas, allowing the objectives to be fulfilled with a broader and more practical overview than usual in other Engineering Schools.
Assessment Methods
Examination 40%
Assignment and Report 60%.
Assessment Methods
Examination 40%
Assignment and Report 60%.
Teaching Staff
- António Rui de Oliveira Santos Silva Melro [responsible]
Certificações
