Computational Modelling of Materials
Code
5278
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Ciências dos Materiais
Credits
6.0
Teacher in charge
Guilherme António Rodrigues Lavareda, Maria do Carmo Henriques Lança
Weekly hours
5
Total hours
79
Teaching language
Português
Objectives
The course intends to implement knowledge and develop basic skills, using computational methods, to simulate and analyze simple models of systems behavior or processes evolution.
Prerequisites
To have basic knowledge of Mathematics, Materials Science and Computation (not restrictive)
Subject matter
Part I - Introduction to programming for modeling
- Importance of numerical / computational methods in materials engineering and nanotechnology.
- Error Concept in computing. Stopping criterion, tolerance and iterative methods.
a) Introduction to VisualBasic (VB)
- VB variants.
- Visual Basic for Applications (VBA). Flow control structures, logical tests and operation with files.
- Applications in Macros and GUIs.
- Use of Excel-VBA for simple numerical-method applications :
Determination of the roots of equations (1), resolution of systems of equations (2), integration (3) and differentiation (4).
b) Introduction to Matlab
- The development environment and the MatLab language.
- Handling of matrix variables, flow control structures, logical tests and operation with files.
- Scripts, functions and graphical user interfaces (GUIs).
- Application to simple numerical methods:
- Determination of roots of equations (1), resolution of systems of equations (2), integration (3) and differentiation (4).
(1) - sequential search and bisection methods.
(2) - Euler and inverse matrix methods.
(3) - Riemann method.
(4) - Finite Difference Method (introduction - Taylor series of 1st order).
Part II - Computer science: modeling and simulation
Curve fitting of experimental data - the least squares method and Fourier
Root finding for equations, using the Newton-Raphson method
Solving systems of equations. Homogeneous systems: values and eigenvectors.
Integration: trapezoidal rule and Simpson''''s rule
Differentiation: Finite difference (Taylor series - higher order than 1st)
Ordinary differential equations: Initial conditions - Euler method and Runge-Kutta method. Boundary conditions - adaptive methods.
Monte Carlo methods and molecular dynamics: basic introduction
Examples of modeling materials and nanotechnology. Specific case studies.
Bibliography
• Steven C. Chapra, Applied numerical methods with MATLAB for engineers and scientists, 2ª ed., Mc-Graw Hill, New York, 2008
• Desmond J. Higham & Nicholas J. Higham, Matlab guide, 2ª ed., SIAM, Philadelphia, 2005
• Steven C. Chapra & Raymond P. Canale, Numerical methods for engineers, 2ª ed., Mc-Graw Hill, New York, 1988 (edição mais recente 7ª ed)
• John H. Mathews & Kurtis D. Fink, Numerical methods : using MATLAB, 4ª ed., Pearson, New Jersey, 2004
• Cleve B. Moler, Numerical computing with MATLAB, 1ª ed, The MathWorks, Inc, SIAM, Philadelphia, 2004
• Curtis F. Gerald & Patrick O. Wheathley, Applied numerical analysis, 7ª ed., Addison Wesley. Boston, 2004
Scientific articles of significant relevance .
Teaching method
The course will be given in a classroom equipped with computers (one computer per student).
Initial presentation of the subjects followed by immediate application or simultaneous execution of commands.
Resolution of training questionnaires.
Software used:
- Visual Basic for Applications (VBA/excel).
- MatLab.