Computational methods of science
Faculteit  Science and Engineering 
Jaar  2019/20 
Vakcode  WICMS08 
Vaknaam  Computational methods of science 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Computational methods of science  
Leerdoelen  1. The student is able to describe the methods mentioned in the course description and to state the keywords and basic notions. 2. The student is able to apply techniques from (vector) calculus, linear algebra and elementary functional analysis to analyze numerical methods for PDEs. 3. The student is able to argue why analysis of numerical methods is relevant for both the development of new methods and its reliable application to practical problems 4. The students is able to perform calculations with a finite element package. 5. The student is able to decompose a PDE problem in several subproblems, all having their own solution method. Program elementary methods for PDEs in MATLAB. 6. The student is able to connect numerical results to the theory. 

Omschrijving  Engineering problems are often studied by means of computer simulation. This course concerns numerical techniques for applied problems governed by partial differential equations. Many techniques will be seen at work in the program COMSOL, a finite element package for modelling. During the course predefined problems from electromagnetics, fluid dynamics and mechanics have to be worked out to master the theory. Moreover, the students will be challenged to ask research questions themselves while doing the lab exercises. The following aspects are considered: 1. Classification of first and second order PDEs 2. Discretization of partial differential equations, in general consistency, stability and convergence (Lax equivalence theorem) a. Elliptic equations Discretization of selfadjoint operators, variational problems, discrete maximum principle, finitedifference, finitevolume and finiteelement approximations, properties of discrete operators, treatment of boundary conditions, local and global discretization error, higherorder discretizations b. Parabolic and hyperbolic equations, Von Neumann stability analysis, CFL condition, method of lines, explicit and implicit schemes: Forward and backward Euler, BDF methods, CrankNicolson. 3. Solution of sparse systems by iterative methods: stationary methods (Jacobi, Gauss Seidel, SOR, multigrid method) and instationary methods based on Krylov subspaces (GG, GMRES, BiCG), preconditioning. 

Uren per week  
Onderwijsvorm 
Hoorcollege (LC), Practisch werk (PRC), Werkcollege (T)
(The Lab Sessions are mandatory. Deadlines will be set; not meeting a deadline will result in zero points for the associated exercise.) 

Toetsvorm 
Practisch werk (PR), Schriftelijk tentamen (WE)
(The course will be subdivided into three units. Each unit will consist of a practical and a test, which both will be marked, say PRi and Ti for the ith unit. Each PRi and Ti should be greater than 5 to pass. The final mark will be (2*PR1+3*PR2+3*PR3+3*T1+4*T2+5*T3)/20. Each nopass can be repaired. For the practical this is during the next unit and for the test this is in the exam. A pass mark cannot be upgraded by a repair. So, the the final mark stands if all practicals and tests have been passed.) 

Vaksoort  bachelor  
Coördinator  dr. ir. F.W. Wubs  
Docent(en)  dr. ir. F.W. Wubs  
Verplichte literatuur 


Entreevoorwaarden  Prior knowledge and skill in handling basic numerical techniques and programming in MATLAB as taught in Numerical Mathematics 1 are required. Furthermore, basic knowledge of linear algebra and calculus is necessary.  
Opmerkingen  The course is a necessary introduction for those who want to follow the course Computational Fluid Dynamics or Numerical Bifurcation Analysis of Large Scale Systems.  
Opgenomen in 
