Scientific Computing I - Winter 09: Difference between revisions
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(Material for future lectures refer to the lectures from winter term 2008, and will be updated throughout the semester) | (Material for future lectures refer to the lectures from winter term 2008, and will be updated throughout the semester) | ||
; Introduction - Scientific Computing as a Discipline : Oct | ; Introduction - Scientific Computing as a Discipline : Oct 29 | ||
: [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 22 | ; Fibonacci's Rabbits, Classification of Models : <!--Oct 22 --> | ||
: [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 & II - Single Species Models, Analysis of ODE Models : Oct 29, Nov 5 | ; Continous Population Models I & II - Single Species Models, Analysis of ODE Models : <!-- Oct 29, Nov 5 --> | ||
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/population.pdf slides] | : [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] | : Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/popmodel.mws popmodel.mws] | ||
; Continous Population Models III & IV - Systems of ODE, Analysis of ODE Systems | ; Continous Population Models III & IV - Systems of ODE, Analysis of ODE Systems | ||
: Nov 5, Nov 12 | : <!-- Nov 5, Nov 12 --> | ||
: [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] | : [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] | : 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 19 & 26, Dec 3 | ; Numerical Methods for ODE : <!-- Nov 19 & 26, Dec 3 --> | ||
: [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] | : [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] | : 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 3, Dec 10 | ; Discrete Models for the Heat Equation : <!-- Dec 3, Dec 10 --> | ||
: [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] | : [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] | : Maple worksheet: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/poisson2D.mws poisson2D.mws] | ||
; Heat Equation - Analytical and Numerical Solution : Dec 10,17 | ; Heat Equation - Analytical and Numerical Solution : <!-- Dec 10,17 --> | ||
: [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] | : [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] | : 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]) | : 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]) | ||
; Discretisation of PDEs, Finite Element Method : Jan 7, 14, 21 | ; Discretisation of PDEs, Finite Element Method : <!-- Jan 7, 14, 21 --> | ||
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/pde_discr.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/pde_discr_6up.pdf handout] | : [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/pde_discr.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/pde_discr_6up.pdf handout] | ||
: Maple worksheets: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/poisson2D.mws poisson2D.mws], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/fe.mws fe.mws] | : Maple worksheets: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/poisson2D.mws poisson2D.mws], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/maple/fe.mws fe.mws] | ||
; Grid Generation : Jan 28 | ; Grid Generation : <!-- Jan 28 --> | ||
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/gridgen.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/gridgen_6up.pdf handout] | : [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/gridgen.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/gridgen_6up.pdf handout] | ||
; Case Study - Computational Fluid Dynamics (not included this year) | ; Case Study - Computational Fluid Dynamics (not included this year) | ||
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/study_cfd.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/study_cfd_6up.pdf handout] | : [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/study_cfd.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/study_cfd_6up.pdf handout] | ||
; Conclusion and Outlook : Feb 28 | ; Conclusion and Outlook : <!-- Feb 28 --> | ||
: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/outlook.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/outlook_6up.pdf handout] | : [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/outlook.pdf slides], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws08/slides/outlook_6up.pdf handout] | ||
Revision as of 07:36, 22 October 2009
- Term
- Winter 09
- Lecturer
- Prof. Dr. Michael Bader
- Time and Place
- Thursday, 9-12, lecture room MI 02.07.023 (first lecture Oct 29; the lecture will be held with 3 hours per week, but will finish before christmas)
- Audience
- Computational Science and Engineering, 1st semester (Module IN2005)
- Tutorials
- -
- Exam
- written exam (t.b.a.)
- Semesterwochenstunden / ECTS Credits
- 2 SWS (2V) / 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 Scientific Computing 1 is intended for students in the Master's Program Computational Science and Engineering. Students in all other study programs, please consider our lecture Modellbildung und Simulation (see the lecture from summer term 2008, for example), instead.
Lecture Notes and Material
(Material for future lectures refer to the lectures from winter term 2008, and will be updated throughout the semester)
- Introduction - Scientific Computing as a Discipline
- Oct 29
- slides, handout
- Fibonacci's Rabbits, Classification of Models
- slides, handout
- Continous Population Models I & II - Single Species Models, Analysis of ODE Models
- slides
- Maple worksheet: popmodel.mws
- Continous Population Models III & IV - Systems of ODE, Analysis of ODE Systems
- slides, handout population models
- Maple worksheets: lotkavolt.mws, dirfields.mws
- Numerical Methods for ODE
- slides, handout
- Maple worksheet: numerics_ode.mws
- Discrete Models for the Heat Equation
- slides, handout
- Maple worksheet: poisson2D.mws
- Heat Equation - Analytical and Numerical Solution
- 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)
- Discretisation of PDEs, Finite Element Method
- slides, handout
- Maple worksheets: poisson2D.mws, fe.mws
- Grid Generation
- slides, handout
- Case Study - Computational Fluid Dynamics (not included this year)
- slides, handout
- Conclusion and Outlook
- slides, handout
Exam
- Date of final exam: t.b.a.
- Helping material: you are allowed to use one sheet (size A4) of paper with hand-written(!) notes during the exam. Any further helping material (books, calculators, etc.) is forbidden!
- Exam topics are all topics covered during the lectures; see the catalogue of exam questions and previous years' exams below.
- Repeat exam: a repeat exam will offered (only for students who failed the regular exam) in April or May 2010. The exam will be written or oral, depending on the number of participants.
Catalogue of Exam Questions
The following catalogue contain questions collected by students of the lectures in winter 05/06 and 06/07. The catalogue is intended for preparation for the exam, only, and serves as some orientation. It's by no means meant to be a complete collection.
Last Years' Exams
Please, be aware that there are always slight changes in topics between the different years' lectures. Hence, the previous exams are not fully representative for this year's exam.
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
Online Material
- Website for the book of A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science
- Maple Computational Toolbox Files: contains an introduction worksheet to Maple plus several worksheets related to CSE, which are covered in this textbook.