Advanced Computional Methods

Recommended Prerequisites

2^nd cycle.

Teaching Methods

Teaching methods of theoretical lessons aim at the global learning of the course. These classes will be taught based on presentations and basic bibliography, using audiovisual means. Students will be called in order to discuss fundamental concepts and those of greater complexity.

In theoretical-practical lessons students must program, some fire safety engineering in buildings situations (FSEB), applying the theoretical concepts taught in classes. Therefore students will perform a set of programming works about different aspects in FSEB such as evacuation, fire propagation and development taking into account smoke movement, and modeling of structures under fire situation. Problems must be demanding but with a workload compatible with the available time.

Learning Outcomes

Targeted phenomena of fire safety engineering, for its high complexity, require advanced knowledge of mathematical modeling. The stochastic nature of the phenomena, multiple dimensions of problems, special nature of valuables involved (safety and human life, property and environmental valuables, etc.) demands approaches where several kinds of knowledge, techniques and tools converge.

One of the objectives of this course is to give students mathematical modeling tools, always from the perspective of their applicability to the phenomena in question, providing them a better understanding and management of these phenomena and possible pioneering contributions to innovation in its modeling.

Aspects related with applications of systems theory and numerical methods with high potential for application to modeling the phenomena related to decision and quantitative analysis, useful to phenomena related to fire safety, will be contemplated.

Work Placement(s)

No

Syllabus

1. Theory of Systems

Introduction

Special features in modeling the reality

Linear programming

Graph theory and networks - Applying to the determination of optimal paths (movement, evacuation, etc.).

Cost-benefit analysis (the problem of intangibles such as human life, environmental valuables, historical property)

Multicriteria Decision Support Methods (discrete and continuous problems, mathematical models to design problems with multiple objectives – safety, distance, time, cost, etc.)

Principles of Stochastic Optimization. Technical approach to combinatorial problems

2. Numerical Methods

Introduction.

Numerical solution of differential equations.

• Introduction to Finite Difference Method.
• Introduction to Finite Elements Method.
• Introduction to Boundary Element Method.
• Fourier Transform.
• Monte Carlo method.

Programming methodology.

Head Lecturer(s)

Fernando Pedro Simões da Silva Dias Simão

Assessment Methods

Assessment
carrying out a set of works: 100.0%

Bibliography

O’ Connor, P. D. T. – Practical Reliability Engineering. John Willey & Sons, 1984.

Hall, J. R. – Probability Concepts.  The Fire Protection Handbook, NFPA, Boston.

Hall, J. R. – Reliability. The Fire Protection Handbook, NFPA, Boston.

Hall, J. R. – Statistics.  The Fire Protection Handbook, NFPA, Boston.

Kleinrock, L. – Queueing Systems.  Volume II: Computer Applications.  NY, 1976.

Murty, K. – Operations Research – Deterministic Optimization Models.  Prentice-Hall, 1995.

Neweel, G. F. – Applications of Queuing Theory, London, 1990.

Philips, D.; Diaz, A.– Fundamentals of Network Analysis. Prentice-Hall, 1981.

Ramachandran, G. – Utility Theory - The Fire Protection Handbook, Boston.

Ramachandran, G. – Value of Human Life.  The Fire Protection Handbook, NFPA, Boston.

Steuer, R. - Multiple Criteria Optimization: Theory, Computation and Application. Wiley, 1986.

Numerical Recipes: The Art of Scientific Computing, 3^rd ed., Cambridge University Press, 2007.