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 Course module: 201900074
 201900074Fundamentals of Numerical Methods (FNM)
 Course info Schedule
Course module201900074
Credits (ECTS)5
Course typeCourse
Language of instructionEnglish
Contact persondr.ir. E.T.A. van der Weide
E-maile.t.a.vanderweide@utwente.nl
Lecturer(s)
 Examiner dr.ir. E.T.A. van der Weide Contactperson for the course 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
 Participating study
 Master Robotics
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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Instructional modes
 Lecture
Tests
 Written examination
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