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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. Mechanical Systems

PDEs

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

FMM

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

.ipynb

The Poisson Equation

22. The Poisson Equation#

A typical elliptic partial differential equation is the Poisson equation.

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21. Partial differential equations

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22.1. Solving the Poisson Equation

By J. Schöberl

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