NDAK12006U Computational Methods in Simulation

Volume 2013/2014
Education
MSc programme in Computer Science
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 smoothed particle hydrodynamics (SPH), finite difference approximations (FDM), finite volume method (FVM) and finite element method (FEM) etc.
Learning Outcome
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
Skills
  • Generate computational meshes
  • Apply finite element method (FEM) on a PDE
  • Apply finite volume method (FVM) on a PDE
  • Apply finite difference method (FDM) on a PDE
  • Apply smoothed particle hydrodynamics (SPH) on a PDE
Knowledge
  • Computer Simulation
  • Theory of discretization methods (FEM, FVM, FDM and SPH) 
Literature
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.
Mixture of lectures, study groups and project group work with hand-ins.
  • Category
  • Hours
  • Lectures
  • 21
  • Practical exercises
  • 49
  • Preparation
  • 36
  • Project work
  • 100
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Continious assessment with grading according to the 7-step scale using internal grading based on written assignments and at least one oral presentation in class.
Marking scale
7-point grading scale
Censorship form
No external censorship
Re-exam
Re-handing-in of written assignments and one 15 minute oral presentation.
Criteria for exam assesment

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.
  • Explain how smoothed particle hydrodynamics (SPH) works.
  • 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.