NDAK12006U Computational Methods in Simulation (CMIS)
MSc programme in Computer Science
MSc programme in Physics
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.
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)
See Absalon when the course is set up.
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.
- Category
- Hours
- Lectures
- 21
- Practical exercises
- 49
- Preparation
- 36
- Project work
- 100
- Total
- 206
As
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Continuing Education - click here!
- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessmentContinious 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
- 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.
Course information
- Language
- English
- Course code
- NDAK12006U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 4
- Schedule
- C
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Computer Science
Course responsibles
- Kenny Erleben (5-6d6770707b42666b306d7730666d)