Computational Mechanics
Faculteit  Science and Engineering 
Jaar  2020/21 
Vakcode  WMME01705 
Vaknaam  Computational Mechanics 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester I b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Computational Mechanics  
Leerdoelen  At the end of the course, the student is able to: 1) Describe the methods mentioned in the course description and to state the keywords and basic notations. 2) Understand/Apply techniques from (vector) calculus, linear algebra and elementary functional analysis to analyze numerical methods for PDEs (e.g well posedness, timestability). 3) Perform calculations with a finite element package (COMSOL) for a variety of mechanical engineering problems. 4) Check whether convergence is according to the theory. 5) Connect outcomes of computations to physics and properties of PDEs. 

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 modeling. The following aspects are considered: 1. Weak formulation of PDEs (Galerkin approximation, LaxMilgram theorem) 2. Finite element method (mass and stiffness matrices, linear and quadratic elements, quadrature rules). 3. Verification of convergence theory in practical problems. 4. Experimenting with COMSOL for a variety of engineering problems. 5. Finite difference and finite volume methods for elliptic PDEs 6. Verification of convergence and conservation properties of a Finite Volume method application. 7. Parabolic and hyperbolic equations, Von Neumann stability analysis, method of lines, explicit and implicit schemes: Forward and backward Euler, BDF methods, CrankNicolson. 8. Vibrations: Eigenvalue problems associated with PDEs. 

Uren per week  
Onderwijsvorm 
Hoorcollege (LC), Practisch werk (PRC), Werkcollege (T)
(26 LC, 8 T, 16 PRC, self study 90) 

Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE), Tussentoets (IT)
(35% WE, 25% IT, 40% AST) 

Vaksoort  master  
Coördinator  G. Li, PhD.  
Docent(en)  G. Li, PhD. ,dr. ir. F.W. Wubs  
Verplichte literatuur 


Entreevoorwaarden  Numerical maths 1 (interpolation, num. integration), multivariate calculus (Gauss theorem, etc), linear algebra (linear spaces, eigenvalues), and familiarity with notations for PDEs. 

Opmerkingen  There will be three assignments/practicals, the grades of which are indicated below by P1, P2, and P3. The grade for each of them should be at least a 5. There will be two tests, grades indicated below by T1 and T2: the intermediate test and the test at the written exam. The grade for each should be at least a 5. The final score is (10*P1+15*P2+15*P3)+25*T1+35*T2)/100. 

Opgenomen in 
