Computational Methods in Simulation (CMIS)

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. Example teaching material is available from 

https://diku-dk.github.io/cmis-online/

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.