Computational methods of science
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Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBMA00405 
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 notations. 2. The student is able to understand/apply techniques from (vector) calculus, linear algebra and elementary functional analysis to analyze numerical methods for PDEs (e.g wellposedness, timestability). 3. The student is able to implement numerical methods for PDEs in a computer programme, e.g. MATLAB. 4. The students is able to perform convergence and stability analysis of numerical methods for PDEs. 5. The student is able to 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. 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. Convergence analysis of Finite Element methods (Cea's Lemma) 4. Implementation of a simple Finite Element method in MATLAB. 5. Finite difference and finite volume methods for elliptic PDEs 6. Convergence analysis of finite difference and volume methods: consistency, stability (Lax equivalence theorem) 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), 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 
Opdracht (AST), Practisch werk (PR), Schriftelijk tentamen (WE)
(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.) 

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


Entreevoorwaarden  Prior knowledge assumed: Numerical maths 1 (interpolation, num. integration). Multivariate calculus (Gauss theorem, etc). Linear Algebra (linear spaces, eigenvalues). Num. Math 2. (Solution of sparse linear systems). Familiarity with basic notions for PDEs (Classification: Elliptic, parabolic, hyperbolic equations; basic knowledge of wellposedness of PDEs)  
Opmerkingen  It is a necessary introduction to the master courses Computational Fluid Dynamics and Numerical Bifurcation Analysis of Large Scale Systems, Finite Element Methods for Fluid Dynamics, Finite element modelling for advanced processing, and Computational Fluid Dynamics. The Lab Sessions are mandatory. Deadlines will be set; not meeting a deadline will result in zero points for the associated exercise. A pass mark cannot be upgraded by a repair. So, the the final mark stands if all practicals and tests have been passed. 

Opgenomen in 
