Numerical Methods

Year
1
Academic year
2011-2012
Code
03005370
Subject Area
Cross-curricular
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Compulsory
Level
3rd Cycle Studies

Recommended Prerequisites

2nd Cycle Studies.

Teaching Methods

The theoretical contents of the curricular unit will be presented through lectures illustrated whenever possible with practical cases. Students are encouraged to apply the competences acquired through practical activities, including the analysis of case studies and exercises.

Learning Outcomes

This course involves the contact with mathematical and classical and advanced numerical methods. The principal aim is to provide skills for the exercise of theoretical and computational research.

Work Placement(s)

No

Syllabus

1. Numerical solution of linear differential equations
Single step and multistep methods. Finite Difference Method: Concept of finite differences, approximations to 1st, 2nd and nth order derivatives, one- and two-dimensional problems, boundary conditions, time variable.
2. Introduction to Finite Element Method
Approximation to the solution of differential equations; Galerkin method; shape functions; types of elements; mapping; Numerical integration.
3. Introduction to Boundary Element Method
Advantages and disadvantages of the FEM, integral equation; premises, fundamental solution; problems of heat conduction, percolation of water, wave propagation.
4. Introduction to Meshless Methods
Basics approach; no mesh; nodal description; methods based on approximations of global type: methods using radial basis functions, methods of Trefftz and of the fundamental solutions; problems of heat conduction, percolation of water, wave propagation.

Head Lecturer(s)

António José Barreto Tadeu

Assessment Methods

Continuous assessment
The analysis of case studies and exercises.: 100.0%

Bibliography

- Steven C. Chapra, Raymond P. Canale – Numerical Methods for Engineers, McGraw-Hill International, ISBN 0-07-079984-9, 1990.

- Negrão, J. – Métodos Discretos de Análise Estrutural, DEC-FCTUC, 1987.

- Heitor Pina – Métodos Numéricos, McGraw-Hill, ISBN 972-9298-04-8, 1995.

- O.C. Zienkiewicz, K. Morgan – Finite Elements and Approximation, John Wiley & Sons, 1983, USA.

- Oñate, E., - Structural Analysis with the Finite Element Method. Linear Statics. Volume 1. Basis and Solids, CIMNE, Springer, ISBN: 978-1-4020-8732-5, 2009.

- K.-J. Bathe, E.L. Wilson – Numerical Methods in Finite Element Analysis, ISBN 0-13-627190-1, 1976.

- Bathe, K. - Finite Element Procedures, Prentice Hall, ISBN: 0-13-301458-4, 1996.

- Brebbia, C.A. - The Boundary Element Methods for Engineers, Pentech Press, London, 1978.

- Brebbia e Dominguez - Boundary Element Method: an Introductory Course, CMP Publications, 1994.