autumn 2018

## STE6239 Simulation - 5 stp

## Course contents

Diverse concepts and methods of applied mathematics, numerical analysis and approximation theory, including aspects of optimal control, game theory, Monte Carlo methods, computational fluid dynamics (CFD), finite and boundary element methods (FEM/BEM), etc.

Argument-based selection of a best approach for modelling and simulation in a given context among several alternatives.

## Objective of the course

**Learning outcomes, skills and attitudes **

On completion of the course, the successful student is expected to have attained the following:

**Knowledge **

Well systematized knowledge of fundamental terminology, definitions, concepts, ideas, methods and results needed to formulate mathematical models, to develop symbolic implementations and/or numerical approximations of these models that can be simulated numerically, with respective verification and, if necessary, tuning and upgrading.

Getting acquainted with a rich diversity of concrete case of modelling and simulating mechanisms and processed from various fields of natural and engineering sciences, on macro and micro (including nano-) level. Main emphasis is on modelling with boundary-value problems for linear and non-linear partial differential equations of elliptic, parabolic, hyperbolic and mixed type, and their numerical solutions, together with analysis of the performance of these models in simulation (stability, order of accuracy, compexity, etc.)

**Skills **

Ability to use the acquired knowledge to perform mathematical modelling and computer simulation of mechanisms and processes.

Ability to assess the performance and verify the fidelity of the results of computer simulations.

Acquiring mathematic modelling and algorithmic implementation skills using the tutorials, methods, algorithms and software of SageMath (http://www.sagemath.org/).

Ability to represent simulation results via scientific visualization, using SageMath.

**General competence **

A holistic understanding of the iterative nature and main components of the entire process of mathematical modelling and numerical simulation, with verification and scientific visualization of the results, and incorporating thses results with larger cooperation projects.

Versatility in cooperation in joint projects of research and development teams.

Versatility in communication of concepts, ideas and methods of mathematical modelling and numerical simulations. Some of the best students in this course, who later choose a topic in computer simulations for their master diploma thesis project, will be expected to communicate their results at international conferences.

## Assessment

**Course work requirement:** 10 homework assignments, 1 per teaching day, given at the end of the teaching day, and due the following teaching day.

For the first 9 homework assignments, the solution of an assignment for a given teaching day is discussed in class at the beginning of the next teaching day.

The last, 10th, homework assignment is, as follows: a set of "model exam" problems, several days prior to the actual exam, is posted at the course website at the end of the second self-study week, for the purpose of the students' self-assessment of their level of preparedness (the solution of the "model exam" is posted on the course website approximately 24 hours after the posting of the formulations of the model problems).

The only compulsory test, the outcome of which is to be delivered to the exam office and which fully determines the course grade, is the final actual exam.

**Examination and assessment:** Written academic exam, 3 hours; assessment grades are A-F, where F is not passed.

Continuation is granted for students who have not passed the last regular exam in this subject; a re-sit exam for this course will be arranged for these students.

## Date for examination

Simulations - written exam 14.12.2018The date for the exam can be changed. The final date will be announced in the StudentWeb early in May and early in November.

## Schedule

## Recommended reading/syllabus

**Course materials, literature and references**

Detailed curriculum/syllabus with time schedule - announced by the lecturer at the beginning of the course lectures.

A comprehensive, self-consistent, stand-alone course website which serves as an online compendium. The uniform resource locator (URL) of the course's main web page within Canvas is announced by the lecturer at the beginning of or during, the course lectures.

A structured collection of optional materials for further reading on the different topics in the course - posted on the course website.