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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
17.1. Implementing a Newton solver
17.2. Coding the Implicit Euler method
17.6. Automatic Differentiation
18. Runge-Kutta methods
19. Mechanical Systems
PDEs
20. Partial differential equations
21. The Poisson Equation
21.1. Solving the Poisson Equation
21.2. Boundary Conditions
21.3. Approximation of functions
21.4. The electric field in a capacitor
21.5. Iterative Solvers
22. Time-dependent equations
22.1. Heat Equation
22.2. Various methods for the Heat Equation
22.3. Wave Equation
22.4. Verlet time-stepping and Mass-lumping
22.5. Waveguides
23. Elasticity
23.1. Modeling Elasticity
23.2. Newton’s method
23.3. Solving nonlinear Elasticity
23.4. 3D Solid Mechanics
23.5. Elastodynamics with Newmark time-stepping
23.6. Forces and Moments
23.7. Meta-material with negative
\(\nu\)
23.8. Exercises
24. Navier Stokes Equations:
24.1. Stokes Equation
24.2. Instationary transport equation
24.3. Benchmark: Flow around a cylinder
24.4. NACA airfoil
24.5. Tesla Valve
25. Maxwell’s equations
25.1. Magnetostics
25.2. A simple coil
25.3. An advanced coil
25.4. Exercises
25.5. The function space H(curl)
25.6. The de Rham complex
25.7. Ranks of discrete operators
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
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Automatic Differentiation
17.6.
Automatic Differentiation
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