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# Introduction to Scientific Computing ## Max Emans

### Time and Place:

Wednesday 11:30-13:00, lecture room 02.07.023, first lesson Oct 22

### Final Exam:

Tuesday, Feb 17 2004, 12:00-14:00, lecture room 02.07.023.

### 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. Starting from mathematical models (derivation, analysis, and classification; various examples), their numerical treatment is discussed (discretization of differential systems, grid generation). The next chapter deals with the efficient implementation of numerical algorithms, both on monoprocessors and parallel computers (architectural features, parallel programming, load distribution, parallel numerical algorithms). Finally, some remarks on the interpretation of numerical results (visualization) are made. 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:

##### Solvers for Systems of Linear Equations

For further material (online script and last year's exercises), please refer to CSE's Virtual Teaching Centre.

### Tutorial:

Monday 11-13, lecture room 02.07.023, first tutorial Oct 27

#### Maple-Worksheets

 topic worksheet completed worksheet Introduction to Maple tutorial.mws - Handling of differential equations by Maple introduction.mws introduction_sol.mws Modelling population growth growtheq.mws growtheq_sol.mws Numerical Treatment of Ordinary Differetial Equations numerical_ode.mws numerical_ode_sol.mws PDE: Poisson's equation in 1D poisson1D.mws - PDE: Heat equation in 1D heat1D.mws - - explicit schemes heat1D_disc.mws - - implicit schemes heat1D_impl.mws - - leap-frog scheme heat1D_leap.mws - PDE: Poisson's equation in 2D poisson2D.mws - Gauss-Seidel and Jacobi relaxation relaxation.mws - Multigrid multigrid.mws -

#### Literature

• 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: Iterative Solution of Large Sparse Systems of Equations, Springer, 1993
• Hackbusch: Elliptic Differential Equations - Theory and Numerical Treatment, Springer, 1992