Scientific Computing I - Winter 11

Term

Winter 11

Lecturer

Dr. rer. nat. habil. Miriam Mehl

Time and Place

Thursday, 10:00-12:00; Hörsaal im LMU Physik Werkstattgebäude Am Coulombwall 1 (Garching!)

Audience

Computational Science and Engineering, 1st semester (Module IN2005)

Tutorials

-

Exam

written exam

Semesterwochenstunden / ECTS Credits

2 SWS (2V) / 3 Credits

TUMonline

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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

Lecture Notes and Material

October 20	no lecture (SET)
October 27	Introduction Population Modelling - Discrete Models	Further Reading: A Real World Application Example Models in Science (Stanford Encyclopedia of Philosophy)
November 3	Population Modelling - ODEs	Further Reading: Analysis of ODE Models
November 10	Population Modelling - ODEs 2	Further Material: Online Slope Field Plotter
November 17	ODE Numerics	Further Reading: Adaptive Time Stepping & Computational Stability
November 24	ODE Numerics Continued
December 1	Parallel Timestepping	Further Reading: The Parareal Algorithm - A Survey of Present Work
December 8	no lecture, Dies Academicus
December 15	Heat Transport Solving the Heat Equation	Further Reading: The heat equation with partial differential equations
December 22	Numerics of PDEs	A gentle introduction to the finite element method
January 12	Numerics of PDEs continued
January 19	Computational Grids	Further Reading: Delaunay Triangulation Advancing Front Method
January 26	Algorithms and Data Storage for PDE Solvers Literature Books and Papers B. DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 1992 (excellent online material) A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science, Princeton University Press (in particular Chapter 3,5,6) G. Golub and J. M. Ortega: Scientific Computing and Differential Equations, Academic Press (in particular Chapter 1-4,8) D. Braess: Finite Elements. Theory, Fast Solvers and Applications in Solid Mechanics, Cambridge University Press (in particular I.1, I.3, I.4, II.2) Tveito, Winther: Introduction to Partial Differential Equations - A Computational Approach, Springer, 1998 (in particular Chapter 1-4,7,10) Online Material Website for pre-2005 courses in Scientific Computing (more extensive - several of the topics have moved to other lectures, or are reduced in extent, now); website is accessible from the "Rechnerhalle" or with login/password (contact lecturer) 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. ODE Software for Matlab (website by J.C. Polking, Rice University)