NDAK12006U Computational Methods in Simulation (CMIS)

Volume 2024/2025
Education

MSc Programme in Computer Science
MSc Programme in Physics

Content

Computational methods in simulation are 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 modeling 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 and also at the 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.

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

 

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 in Python and Matlab. It is 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. Hence, experience with setting up experiments and writing reports is expected.

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.
A mixture of lectures, study groups, and project group work with individual hand-ins.
  • Category
  • Hours
  • Lectures
  • 21
  • Preparation
  • 36
  • Exercises
  • 49
  • Project work
  • 100
  • Total
  • 206
Written
Oral
Individual
Collective
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes (no preparation)
Type of assessment details
The exam takes an outset in theory taught over the course. Students should be able to derive theory/math on the blackboard during the examination
Exam registration requirements

To qualify for the exam the student must complete 3 out of a maximum of 4 short reports which can be made as a group or as individual reports. The written reports should be maximally 10 pages.

Aid
Without aids
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Re-exam

The reexam format and qualification for reexam are the same as for the regular exam. The reports must be submitted no later than two weeks before the re-exam week to qualify for the re-exam.

 

Criteria for exam assesment

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