Computational Methods in Simulation (CMIS)

Course content

Computational methods in simulation is an important computer tool in many disciplines like bioinformatics, scientific computing, and computational physics, computational chemistry, computational biology, computer animation and many more. A wide range of problems can be solved using computational methods like biomechanical modelling of humans such as computing the stress field of bones or computational fluid dynamics solving for the motion of liquids, gasses, and thin films. Dealing with the motion of atoms and molecules using molecular dynamics. Computing the dynamic motion of Robots or mechanical systems and many more.

This course will build up a toolbox of simulation methods that the student can use when building solutions in his or her future studies. Therefore this course is an ideal supplement for students coming from many different fields in science.

This course aims to create an overview of typically used simulation methods and techniques. The course seeks to give insight into the application of methods and techniques on examples such as the motion of deformable models, fluid flows, heat diffusion, etc. During the course, the student will be presented with mathematical models such as a system of partial differential equations. The course seeks to teach the student the classical approaches to reformulate and approximate mathematical models in such a way that they can be used for computations on a computer.

This course teaches the basic theory of simulation methods. The focus is on deep learning of how the methods covered during the course works. Both at a theoretical level but also at implementation level with a focus on computer science and good programming practice.

There will be weekly programming exercises where students will implement the algorithms and methods introduced from theory and apply their implementations to case-study problems like computing the motion of gas or granular material.

The course will cover topics such as finite difference approximations (FDM), finite volume method (FVM) and finite element method (FEM), etc.

Education

MSc Programme in Computer Science
MSc Programme in Physics

Learning outcome

Knowledge of

  • Computer Simulation
  • Theory of discretization methods (FEM, FVM, FDM, etc)

 

Skills to

  • Apply the finite element method (FEM) on a PDE
  • Apply the finite volume method (FVM) on a PDE
  • Apply the finite difference method (FDM) on a PDE

 

Competences to

  • Apply a discretization method to a given partial differential equation (PDE) to derive a computer simulation model
  • Implement a computer simulator using a high-level programming language

 

A mixture of lectures, study groups, and project group work with individual hand-ins.

See Absalon when the course is set up.

It is expected that students know how to install and use Python or Matlab by themselves. Any programming language is allowed, but we only offer help and teacher solutions in Python and Matlab. It is also expected that students know what matrices and vectors are and that students can differentiate vector functions.

Academic qualifications equivalent to a BSc degree is recommended.

Theorems like fundamental theorem of calculus, mean value theorem or Taylors theorem will be used during the course. The inquisitive students may find more in-depth knowledge from Chapters 2, 3, 5, 6 and 13 of R. A. Adams, Calculus, 3rd ed. Addison Wesley.

Written
Oral
Individual
Collective
Continuous feedback during the course of the semester

There will be written individual feedback on hands-ins. Oral feedback consists of plenum collectively feedback discussions about common trends and mistakes in hands-ins. The flipped classroom offers students many possibilities for their initiative to discuss their learning progress and learning challenges with teachers as a continuous feedback option.

ECTS
7,5 ECTS
Type of assessment
Continuous assessment
Continuous assessment based on 7-8 written assignments weighted equally.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Criteria for exam assessment

To obtain the grade 12 the student should convincingly and accurately demonstrate the knowledge, skills, and competences described under Learning Outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 21
  • Preparation
  • 36
  • Exercises
  • 49
  • Project work
  • 100
  • English
  • 206