Christoph Pfrommer

Modern Computational Astrophysics: Concepts and Applications
The objectives of this course are to endow students with the capacity
to identify and classify common numerical problems in modern
astrophysics. The course aims at an active understanding of numerical
methods and algorithms as well as their ranges of
applicability. Solving basic astrophysical problems with adequate
numerical techniques and determining the range of validity is an
essential part of the course. This course (PHY755) presents
theoretical concepts which are then practiced in course PHY765. A
participation of both courses is strongly recommended.
Lecturers:
Prof. Christoph Pfrommer & Dr. Philipp Girichidis
Place and Dates: The lectures take place every Tuesday, at
14:1515:45 in room 2.28.0.087. The exercise classes take place in the
same room immediately after the lectures, 16:0017:30.
The lectures are based on the revised lecture notes originally written
by Prof. Springel (MaxPlanck Institute for Astrophysics) and are
available as
a
PDF file (password protected).
Contents:
 Reviewing basic concepts of numerical simulations (preparatory course)
 Integer arithmetic
 Floating point arithmetic
 Integration of ordinary differential equations
 The Euler method: explicit and implicit
 RungeKutta methods and adaptive step sizes
 The leapfrog and symplectic integrators
 Collisionless particle systems
 Nparticle ensembles
 Uncorrelated (collisionless) systems
 Nbody models of collisionless systems
 Tree algorithms
 Multipole expansion
 Hierarchical grouping
 Tree walk
 The particlemesh technique
 Mass/charge assignment
 Solving for the potential and force calculation
 Interpolating from the mesh to the particles
 Fourier transform techniques
 Convolution problems
 The discrete Fourier transform
 Nonperiodic problems with 'zero padding'
 Basic gas dynamics
 Basic conservation laws
 Euler and NavierStokes equations
 Shocks, fluid instabilities and turbulence
 Eulerian hydrodynamics
 Types and solution schemes of partial differential equations
 Advection and the Riemann problem
 Finite volume discretization
 Godunov's method and Riemann solvers
 Extensions to multiple dimensions and highorder accuracy
 Smoothed particle hydrodynamics (SPH)
 Kernel interpolants
 Variational derivation of SPH
 Artificial viscosity
 Advantages and disadvantages of SPH
 Diffusion equation
 Explicit method
 Implicit methods
 Paralellization techniques
 Hardware overview
 Shared memory parallelization with OpenMP
 Distributed memory parallelization with MPI
Homework Assignments
All homework assignments and sample code can be obtained
via this
link (password protected).
 Exercise 1  Ordinary differential equations, due Oct 30, 2018.
 Exercise 2  Collisionless particle systems, due Nov 11, 2018.
 Exercise 3  Tree algorithms, due Dec 04, 2018.
 Exercise 4  Fourier transform and particle mesh techniques, due Dec 11, 2018.
 Exercise 5  Sound waves and shocks, due Dec 18, 2018.
 Exercise 6  Turbulence and Sedov explosion, due Jan 08, 2019.
 Exercise 7  Hyperbolic conservation laws (counts twice), due Jan 29, 2019.
 Exercise 8  Diffusion problems, due Feb 5, 2019.
Credit Points:
Credit points for this lectures can be used for the Master Science
Astrophysics Modules PHY755 and PHY750.
Grades and credit points are given on the basis of an oral exam. To be
eligible for this exam, you need to obtain at least 50% of the points
of your homework assignments.
