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Course module: 202000707
202000707
Numerical Methods for PDE
Course info
Course module202000707
Credits (ECTS)2
Course typeStudy Unit
Language of instructionEnglish
Contact personprof.dr.ir. B.J. Geurts
E-mailb.j.geurts@utwente.nl
Lecturer(s)
Lecturer
A.D. Franken
Examiner
prof.dr.ir. B.J. Geurts
Contactperson for the course
prof.dr.ir. B.J. Geurts
Lecturer
prof.dr.ir. B.J. Geurts
Lecturer
K.A. Redosado Leon
Academic year2021
Starting block
2B
Application procedureYou apply via OSIRIS Student
Registration using OSIRISYes
Aims
After passing this course the student;
  • is familiar with the concept of discretization for partial differential equations,
  • can determine the order of accuracy of explicit temporal and spatial discretization methods,
  • knows about numerical stability and can determine time step sizes that lead to stable simulations,
  • can proof convergence of discretization methods, e.g., using the maximum principle,
  • can implement and analyze Dirichlet, von Neumann and Robin boundary conditions,
  • can translate continuous PDE formulations into efficient algorithms, implement and test these and apply the discrete method to simulate time dependent PDE solutions,
  • is familiar with numerical convergence tests and can execute these in detail.
Content
Partial differential equations (PDEs) form a powerful language for modeling many fundamental and applied problems in physics. While some of these problems can be solved entirely using analytical methods, most important problems defy such treatment and need to be addressed differently. In this course, numerical methods for solving the underlying PDEs will be introduced, analyzed in terms of stability and accuracy and implemented in efficient algorithms that can be used to approximate the analytical solution with controlled error level. Combining analytical and numerical methods will provide a strong expertise for any question of fundamental or applied nature in modern physics.
In this introductory course we restrict to problems in one spatial dimension and address problems involving diffusion (parabolic PDEs) and flow (hyperbolic PDEs), that can be treated using explicit time-stepping methods. Apart from numerical convergence analysis, attention is also given to formal convergence proof methods, e.g., based on the maximum principle.


Assessment Plan
T
he assessment plan for this course will be published no later than 2 weeks before the starting block of the course on https://www.utwente.nl/nl/tn/onderwijs/toetsschemas/
 
Assumed previous knowledge
Prior knowledge for this course includes basic first year calculus.
Module
Module 8
Participating study
Bachelor Applied Physics
Required materials
-
Recommended materials
Course material
Copies of slides used during oral lectures
Instructional modes
Lecture

Practical
Presence dutyYes

Presentation(s)
Presence dutyYes

Q&A

Tutorial

Tests
Numerical Methods for PDE

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Kies de Nederlandse taal