Computational Mechanics

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, time-stability). 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, Lax-Milgram 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, Crank-Nicolson. 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	dr. ir. F.W. Wubs
Docent(en)	dr. ir. F.W. Wubs
Verplichte literatuur	Titel Auteur ISBN Prijs Lecture Notes Computational Methods of Science. Fred W. Wubs The Finite Element Method: Linear Static and Dynamic Finite Element Analysis Only a few selected sections are required. Thomas Hughes
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	Opleiding Jaar Periode Type MSc Mechanical Engineering: Advanced Instrumentation  (Compulsory Courses) 1 semester I b verplicht MSc Mechanical Engineering: Materials for Mechanical Engineering  (Compulsory Courses) 1 semester I b verplicht MSc Mechanical Engineering: Process Design for Energy Systems  (Compulsory Courses) 1 semester I b verplicht MSc Mechanical Engineering: Smart Factories  ( Compulsory courses) 1 semester I b verplicht