High performance computing and numerical modeling
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1.    Collisional and collisonless N-body dynamics

      1.1. Relaxation time
      1.2. Gravitational softening
      1.3. N-body equations in cosmology
      1.4. (Symplectic) time integration 

2.   Gravitational force calculation

      2.1. Particle mesh technique
      2.2. Multigrid techniques
      2.3. Multipole methods, aka Tree codes
      2.4. Hybrids

3.   Basic gas dynamics

      3.1. Euler equations
      3.2. Navier-Stokes equations
      3.3. Ideal MHD equations
      3.4. Shocks
      3.5. Fluid instabilities

4.   Eulerian hydrodynamics

      4.1. Finite volume discretization
      4.2. Advection 
      4.3. Riemann problem
      4.4. Godunov's technique
      4.5. High-order extensions

5.   Smoothed particle hydrodynamics

      6.1. Kernel interpolation
      6.2. SPH equations of motion
      6.3. Artificial viscosity
      6.4. New trends in SPH

6.   Moving-mesh techniques

      7.1. Differences between Eulerian and Lagrangian techniques
      7.2. Tessellation techniques
      7.3. Moving-mesh hydrodynamics

7.   Towards high dynamic range

      5.1. Adaptive mesh refinement techniques
      5.2. Hierarchical time integration
      5.3. Treating source terms / Strang splitting

8.   Parallelization techniques and current computing trends

      8.1. Multi-threading and OpenMP
      8.2. MPI
      8.3. GPU computing
      8.4. Towards Exascale