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Introduction to Scientific Computing

Basic Linear Algebra

1. Overview
2. Development environment
3. Refresh your C++
4. Creating documentation
5. Expression templates
6. Automatic testing
7. Python bindings
8. Interfacing Lapack

Performance

9. Overview
10. Vectorization
- 10.1. The SIMD - class
- 10.2. Vectorizing mathematical functions
11. Pipelining
12. Caches
13. Parallelization

ODEs

14. Solving ordinary differential equations
15. A little bit of theory
16. Some simple time-stepping methods
17. Implementation
18. Runge-Kutta methods
19. Mechanical Systems

PDEs

20. Partial differential equations
21. The Poisson Equation
22. Time-dependent equations
23. Elasticity
24. Navier Stokes Equations:
25. Maxwell’s equations
26. Helmholtz Equation
27. Eigenvalue problems
28. Stationary Transport Equation
29. Instationary Transport Equation
30. Navier Stokes Equations
31. Computation of Curvature

FMM

32. Fast Multipole Methods
33. Multipole basis functions
34. Layer potentials

.ipynb

The Poisson Equation

21. The Poisson Equation#

A typical elliptic partial differential equation is the Poisson equation.

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20. Partial differential equations

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21.1. Solving the Poisson Equation

By J. Schöberl

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