Modeling and Computational Engineering MOD510

Knowledge:

• Advanced knowledge of algorithms and algorithmic thinking, and apply it to formulate and solve discrete and continuous problems
• Advanced knowledge in numerical analysis, in order to evaluate the constraints associated with the chosen solution method, including approximation errors
• In depth knowledge of the basic numerical methods

Skills:

• Develop models of physical systems from biology, chemistry, flow in porous media, and geology
• Test models against experimental data, and use data to constrain the model
• Apply appropriate numerical methods to solve mathematical models
• Develop own programs written in the program language Python

General Competence:

• To write scientific reports
• Visualize and presentation of results from numerical simulations
• The use of computers to work more efficiently with large amounts of data

You will learn the most common numerical methods used to solve complex physical, biological, financial or geological phenomena. Examples of methods are numerically derivation, numerical integration, Monte Carlo and boot strapping methods, inverse methods, numerical solution of common differential equations, simulated annealing, lattice Boltzmann models, random walk models, box (compartment) models.

The primary programming language is Python. Through assignments, you will learn how to set up mathematical models of a phenomenon, develop algorithms, implement them, and investigate the strength and limitations of the solution method and the mathematical model. You will learn how to code efficiently in Python, both by using functions and classes. The projects focus on modeling realistic systems, and to compare with measured data to learn more about the systems. The goal of the projects is to reproduce state of the art scientific results.