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Introduction to Scientific Computing
Basic Linear Algebra
1. Overview
2. Clone a project from github
3. Refresh your C++
4. Creating documentation
5. Expression templates
6. Python bindings
7. Interfacing Lapack
Performance
8. Overview
9. Vectorization
10. Pipelining
11. Caches
12. Parallelization
ODEs
13. Solving ordinary differential equations
14. A little bit of theory
15. Some simple time-stepping methods
16. Implementation
17. Runge-Kutta methods
18. Mechanical Systems
PDEs
19. Partial differential equations
20. The Poisson Equation
20.1. Solving the Poisson Equation
20.2. Boundary Conditions
20.3. Approximation of functions
20.4. The electric field in a capacitor
20.5. Iterative Solvers
21. Time-dependent equations
21.1. Heat Equation
21.2. Various methods for the Heat Equation
21.3. Wave Equation
21.4. Verlet time-stepping and Mass-lumping
21.5. Waveguids
22. Elasticity
22.1. Modeling Elasticity
22.2. Newton’s method
22.3. Solving nonlinear Elasticity
22.4. 3D Solid Mechanics
22.5. Elastodynamics with Newmark time-stepping
22.6. Forces and Moments
22.7. Meta-material with negative
\(\nu\)
22.8. Exercises
23. Navier Stokes Equations:
23.1. Stokes Equation
23.2. Instationary transport equation
23.3. Benchmark: Flow around a cylinder
23.4. NACA airfoil
23.5. Tesla Valve
24. Helmholtz Equation
25. Eigenvalue problems
26. Stationary Transport Equation
27. Instationary Transport Equation
28. Navier Stokes Equations
29. Magnetostatics
30. Computation of Curvature
FMM
31. Fast Multipole Methods
32. Multipole basis functions
Index
