Computational Methods in Simulation (CMIS)

Course content

Computational methods in simulation is an important computer tool in many disciplines like bioinformatics, eScience, 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: bio-mechanical modeling of humans such as computing the stress field of bones or computational fluid dynamics solving for motion of liquids, gasses and thin films. Dealing with 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 which 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.

The aim of this course is to create an overview of typically used simulation methods and techniques. The course seek to give insight into the application of methods and techniques on examples such as 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 seek to learn 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 on a theoretical level but also on an implementation level with 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 own implementations to case-study problems like computing the motion of a 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

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

 

Skills

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

 

Competences

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

 

Mixture of lectures, study groups and project group work with hand-ins.

See Absalon when the course is set up.

It is expected that students know how to install and use Matlab by themselves. It is also expected that students know what matrices and vectors are and that students are able to differentiate vector functions.

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.

ECTS
7,5 ECTS
Type of assessment
Continuous assessment
Continuous assessment based on 5-6 written assignments and at least one oral presentation in class.
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Criteria for exam assessment

In order to achieve the highest grade 12, a student must be able to:

  • Describe computational meshes and evaluate their geometric and numerical properties.
  • Apply finite difference method (FDM)on a partial differential equation, and account for approximation and numerical errors.
  • Account for the main principle in the finite volume method.
  • Apply the finite volume method (FVM) on a partial differential equation.
  • Derive the Weighted Residual (Galerkin) Method.
  • Apply the finite element method (FEM) on a partial differential equation.

Single subject courses (day)

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