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Scientific Computing

Lecture with tutorials (4 hours per week, 10 credit points) in winter term 2014/2015.

Dates
Time
Room
Lecturer/Tutor
Lectures
Tue, 8.30 - 10.00
FH 312
Dr. Kersten Schmidt
Thu, 10.15 - 11.45
(every second week)
MA 851
Dr. Kersten Schmidt
Tutorials
Thu, 10.15 - 11.45
(every second week,
starting 30 Oct 2014)
MA 851
Dirk Klindworth
Unix pool1
Tue, 10.00  - 14.00
MA 241
Dirk Klindworth

1During that time you have priority access to 15 Unix pool clients and Dirk Klindworth will be there (11.00 - 13.00) to answer questions.

Topics

  • Linear regression
  • Fast Fourier transform
  • Modelling by partial differential equations (PDEs)

    • Maxwell, Helmholtz, Poisson, linear elasticity, Navier-Stokes equation
    • boundary value problem, eigenvalue problem
    • boundary conditions (Dirichlet, Neumann, Robin)
    • handling of infinite domains (wave-guide, homogeneous exterior: Dirichlet-to-Neumann maps, perfectly matched layers)
    • boundary integral equations

  • Computer aided-design (CAD)
  • Mesh generators
  • Space discretization of PDEs

    • Finite difference method
    • Finite element method
    • Discontinuous Galerkin finite element method

  • Solvers

    • Linear solvers (direct, iterative), preconditioner
    • Nonlinear solvers (Newton-Raphson iteration)
    • Eigenvalue solvers

  • Parallelization

    • SIMP: OpenMP
    • MIMP: MPI

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Lecture notes/slides

 

Supplementary material

  • Example of reduced fill-in when permuting sparse matrices: Python script

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Tutorials

Topics of tutorial classes (preliminary)

  • 30 Oct 2014: Variational formulations of elliptic boundary value problems, notes
  • 4 Nov 2014: Discrete variational problem, finite element meshes and linear finite element space, notes
  • 18 Nov 2014: Assembling of linear finite element matrices/vectors and computation of element matrices/vectors, notes
  • 4 Dec 2014: Implementation of homogeneous and inhomogeneous Dirichlet boundary conditions, notes
  • 18 Dec 2014: Well-posedness and implementation of Poisson problems, notes
  • 15 Jan 2015: Questions and answers
  • 29 Jan 2015: Parallelization in Python
  • 12 Feb 2015: no tutorial class

 

Exercise sheets

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Literature

Regression / Legendre polynomials

  • H.-R. Schwarz and J. Waldvogel, "Numerical Analysis: A Comprehensive Introduction", John Wiley & Sons, 1989. (dt. H.-R. Schwarz und N. Köcker "Numerische Mathematik", Teubner Verlag, 2004.)

 

Fast Fourier transform

  • W.P. Petersen and P. Arbenz, "Introduction to Parallel Computing", Oxford University Press, 2004.

 

Finite element methods

 

Boundary element methods

  • S. Sauter and C. Schwab, "Boundary element methods", Springer-Verlag, 2011.
  • O. Steinbach, "Numerical approximation methods for elliptic boundary value problems", Springer-Verlag, 2008.

 

Computer aided design

  • D. Marsh, "Applied geometry for computer graphics and CAD", Springer-Verlag, 2005.

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Zusatzinformationen / Extras

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Adresse

TU Berlin
Institut für Mathematik
Sekr. MA 6-4
Straße des 17. Juni 136
D-10623 Berlin

So finden Sie uns

Mathematikgebäude (MA)
3. Obergeschoss
Räume 363, 365 u. 379