Scientific Computing I - Winter 08: Difference between revisions

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(Material for future lectures refer to the lectures from winter term 2007, and will be updated throughout the semester)
(Material for future lectures refer to the lectures from winter term 2007, and will be updated throughout the semester)


; Introduction: Scientific Computing as a Discipline : Oct
; Introduction - Scientific Computing as a Discipline : Oct  
: ([http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/discipline.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/discipline_6up.pdf handout])
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/discipline.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/discipline_6up.pdf handout]
; Fibonacci's Rabbits, Classification of Models : Oct
; Fibonacci's Rabbits, Classification of Models : Oct  
: ([http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/fibo.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/fibo_6up.pdf handout])
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/fibo.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/fibo_6up.pdf handout]
; Continous Population Models I -- Single Species Models : Nov
; Continous Population Models I - Single Species Models : Nov  
: ([http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/population.pdf slides], Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/popmodel.mws handout])
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/population.pdf slides]
 
: Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/popmodel.mws popmodel.mws]
; Continous Population Models II & III - Systems of ODE, Analysis of ODE Models
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/population2.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/population_6up.pdf handout population models]
: Maple worksheets: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/lotkavolt.mws lotkavolt.mws], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/dirfields.mws dirfields.mws]
; Numerical Methods for ODE : Nov
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/ode_numerics.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/ode_numerics_6up.pdf handout]
: Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/numerics_ode.mws numerics_ode.mws]
; Discrete Models for the Heat Equation : Dec
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/heatmodel.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/heatmodel_6up.pdf handout]
: Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/poisson2D.mws poisson2D.mws]
; Heat Equation - Analytical and Numerical Solution : Dec
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/heateq.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/heateq_6up.pdf handout]
: Maple worksheets: Fourier's method: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/heat1D_four.mws heat1D_four.mws], Discretisation: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/heat1D_disc.mws heat1D_disc.mws], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/heat1D_impl.mws heat1D_impl.mws]
: Additional material: Neumann stability ([http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/scicomp3.pdf worksheet] with [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/solution3.pdf solution]), discrete energy ([http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/heatenergy.pdf handout])


= Exam =
= Exam =
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* Stoer, Bulirsch: Introduction to Numerical Analysis, Springer, 1996
* Stoer, Bulirsch: Introduction to Numerical Analysis, Springer, 1996
* Hackbusch: Elliptic Differential Equations - Theory and Numerical Treatment, Springer, 1992
* Hackbusch: Elliptic Differential Equations - Theory and Numerical Treatment, Springer, 1992
[[Category:Teaching]]

Revision as of 10:41, 21 July 2008

Term
Winter 08
Lecturer
Dr. Michael Bader
Time and Place
Wednesday, t.b.a., Raum 02.07.023, Beginn: 23.10.2008
Audience
Computational Science and Engineering, 1. Semester
Tutorials
-
Exam
written exam (time and day t.b.a.)
Semesterwochenstunden / ECTS Credits
2 SWS / 3 Credits
TUMonline
{{{tumonline}}}



Contents

This course provides an overview of scientific computing, i. e. of the different tasks to be tackled on the way towards powerful numerical simulations. The entire "pipeline" of simulation is discussed:

  • mathematical models: derivation, analysis, and classification
  • numerical treatment of these models: discretization of (partial) differential systems, grid generation
  • efficient implementation of numerical algorithms: implementation on monoprocessors vs. parallel computers (architectural features, parallel programming, load distribution, parallel numerical algorithms)
  • interpretation of numerical results & visualization
  • validation

The course is conceived as an introduction to the thriving field of numerical simulation for computer scientists, mathematicians, engineers, or natural scientists without an already strong background in numerical methods.

Lecture Notes and Material

(Material for future lectures refer to the lectures from winter term 2007, and will be updated throughout the semester)

Introduction - Scientific Computing as a Discipline
Oct
slides, handout
Fibonacci's Rabbits, Classification of Models
Oct
slides, handout
Continous Population Models I - Single Species Models
Nov
slides
Maple worksheet: popmodel.mws
Continous Population Models II & III - Systems of ODE, Analysis of ODE Models
slides, handout population models
Maple worksheets: lotkavolt.mws, dirfields.mws
Numerical Methods for ODE
Nov
slides, handout
Maple worksheet: numerics_ode.mws
Discrete Models for the Heat Equation
Dec
slides, handout
Maple worksheet: poisson2D.mws
Heat Equation - Analytical and Numerical Solution
Dec
slides, handout
Maple worksheets: Fourier's method: heat1D_four.mws, Discretisation: heat1D_disc.mws, heat1D_impl.mws
Additional material: Neumann stability (worksheet with solution), discrete energy (handout)

Exam

A written exam will be offered at the end of the lecture period.

Literature

  • A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science, Princeton University Press
  • Boyce, DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 1992 (5th edition)
  • Golub, Ortega: Scientific Computing: An Introduction with Parallel Computing, Academic Press, 1993
  • Tveito, Winther: Introduction to Partial Differential Equations - A Computational Approach, Springer, 1998
  • Stoer, Bulirsch: Introduction to Numerical Analysis, Springer, 1996
  • Hackbusch: Elliptic Differential Equations - Theory and Numerical Treatment, Springer, 1992
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