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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
11. Pipelining
12. Caches
- 12.3. Efficient Cholesky factorization
13. Parallelization

ODEs

14. Solving ordinary differential equations
15. A little bit of theory
16. Some simple time-stepping methods
17. Implementation
18. Automatic Differentiation
19. Runge-Kutta methods
20. Automatic step-size control
21. Mechanical Systems

PDEs

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

FMM

34. Fast Multipole Methods
35. Multipole basis functions
36. Layer potentials

.ipynb

The Poisson Equation

23. The Poisson Equation#

A typical elliptic partial differential equation is the Poisson equation.

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22. Partial differential equations

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23.1. Solving the Poisson Equation

By J. Schöberl

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