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Syllabus for

Academic year
TMA632 - Project course: Partial differential equations
 
Owner: TM
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: C
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0101 Examination 5,0 c Grading: TH   5,0 c   Contact examiner,  Contact examiner

In programs

TM Teknisk matematik, Year 2 (elective)
CEMAS MSc PROGRAMME IN COMPUTATIONAL AND EXPERIMENTAL TURBULENCE, Year 1 (elective)
EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)

Examiner:

Professor  Stig Larsson



Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Aim

The course complements the PDE courses within the TM program on differential equations and com-puting. The objective is to give the participant an in-sight of how a finite element software is construc-ted, especially with respect to adaptive FEM.
The course is based on Diffpack, an object oriented software library for scientific computing. By using Diffpack and other suitable software tools will a project be formulated and completed.
The project work integrates applications, numerics, algorithms and software. The course is specifically to TM-students which are going to do thesis work within scientific computing.
CONTENTS AND ORGANISATION OF THE COURSE
Introduction to Diffpack. About C++ and object oriented software development. Menusystem, visu-alization, mesh generation and other tools. FEM formulation for typical boundary value problems. Implementation of model problems. Extensions to time depending and nonlinear problems. Applica-tions to e.g. solid and fluid mechanics. Solution of large linear system of equations. Use of adaptivity, error control and mesh refinement. Project work.

Literature

Hans Petter Langtangen, Computational Partial Differential Equations,
Numerical Methods and Diffpack Programming, Lecture Notes in Computational Science and Engineering, Vol. 2, Springer-Verlag, 1999.

Examination

The examination consists of an independent project. Oral and written presentations of the project.
PRE KNOWLEDGE
TMA 371 Partial Differential Equations TM or equivalent. Programming skills and experience of C++ is advantageous.


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