    Close Help Print  Course module: 201900074  201900074Fundamentals of Numerical Methods (FNM) Course info Schedule   Course module 201900074
Credits (ECTS) 5
Course type Course
Language of instruction English
Contact person dr.ir. E.T.A. van der Weide
E-mail e.t.a.vanderweide@utwente.nl
Lecturer(s)  Contactperson for the course dr.ir. E.T.A. van der Weide   Lecturer dr.ir. E.T.A. van der Weide  Starting block
 1A Application procedureYou apply via OSIRIS Student
Registration using OSIRISYes Aims
 body { font-size: 9pt; font-family: Arial } table { font-size: 9pt; font-family: Arial } After the course the student is able to  Create a numerical method for a partial differential equation (PDE) based on a finite difference or finite element discretization. Indicate the character of a second order PDE (elliptic, parabolic or hyperbolic) and determine what type of discretization method to use. Identify whether or not a special treatment for advection terms is needed. Perform a numerical time integration for an evolution problem. Carry out a Fourier Stability Analysis for parabolic and hyperbolic problems. Content
 body { font-size: 9pt; font-family: Arial } table { font-size: 9pt; font-family: Arial } After a short recapitulation of the required mathematics, the character of linear second order PDE’s is determined via the eigenvalues of the corresponding (symmetric) coefficient matrix. It is shown that any second order PDE can be transformed into the Laplace equation, the heat equation or the wave equation, which are representative for elliptic, parabolic and hyperbolic equations, respectively.   Thereafter, discretization methods are introduced. Both the finite difference method and the finite element method for the discretization of the spatial derivatives are discussed in depth. First the elliptic problems are treated followed by treatment of advection terms.   For the time discretization several explicit and implicit methods are given. It is shown that for parabolic and hyperbolic problems the spatial part can be discretized in a decoupled manner from the temporal part, where finite difference or finite element methods can be used for the former and the time integration schemes for the latter.   The consistency, convergence and stability of numerical methods will be evaluated via Fourier Stability Analysis. Additional info: This is a mathematical oriented course. Working knowledge of Math B1, B2, C1, D1 and D2 is assumed.  Assumed previous knowledge BSc in Mechanical Engineering or equivalent Participating study Master Mechanical Engineering     Participating study Master Sustainable Energy Technology  Required materials
Course material
 PDF file of old lecture notes by R. Hagmeijer Course material
 PDF file for every lecture  Recommended materials
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