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Contents:
Computational simulations are a standard tool in astrophysics. In this
lecture we present basic numerical methods for the simulation of
physical problems based on relevant examples from
astrophysics, exercises in C/C++ are included.
This course is part I of the specialization "Computational
Astrophysics" and comprises 1V1S + 1V1S (each 3 CP,
so in total 6 CP for this course ).
Certificate of attendance:
- without mark, e.g., Master of Astrophysics, module PHY-765
"Topics in Advanced Astrophysics" - this module has in total 8 SWS
with 12 CP, oral exam (45 min) to pass whole module:
at least 1./3. of the total points of the (weekly) exercises
- with a mark (other Master courses):
small programming project at the end of the semester
Subsequent lectures (for the Specialization Track "Computational Astrophysics")
Exercises (pdf):
Most of the exercises are programming tasks in
C/C++. You need access to a Linux (see links below)
or Mac computer for
the tasks with graphical output (X11) or programming
skills in a graphical toolkit under Windows.
You can get an account in the student's computer lab,
which is also accessible via ssh (see Links). Contact me for that.
Hand in solutions (usually source files and PDF/txt files) as
one compressed file (tar.gz, zip). If a task requires an explicit
answer, write the answer in a PDF or txt file. Do not dare to hand
in unfiltered AI output.
- Exercise 1
Plotting data
- Exercise 2
Number representation
- Exercise 3
GRS, Loops, arrays
- Exercise 4
Pointer, arrays, SAT, class complex
- Exercise 5
Numerical errors
- Exercise 6
The Two-Body Problem
- Exercise 7
The Special Three-Body Problem, Runge-Kutta method (RK4)
- Exercise 8
The Kepler problem III, Alternative laws of gravitation,
Lane-Emden equation
- Exercise 9
Roots, interpolation
- Exercise 10 Solution
Integration, derivatives
- Exercise 11 Solution
Geometry, Monte Carlo simulations
- Exercise 12 Solution
Monte Carlo simulations, MC-Integration
- Exercise 13
MC and Parallelization techniques
- Exercise 14
Linear Algebra: Determinants, Systems of Linear Equations
- Exercise 15
Bonus: Applications of MC and Linear Algebra
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Lectures (pdf):
-
Introduction - Working with Unix/Linux
(2.4 MB)
Hands on Linux (286 kB)
Introduction (script) (4 MB)
Detailed informationen about login with SSH and VNC
on the computers of the student's computer cluster:
login_ssh_vnc_en.pdf (931 kB)
gnuplot (778 kB)
FYI: Brief intro to LaTeX (1.5 MB)
-
Review C/C++ (827 kB)
Hands on C++ (177 kB)
-
Errors, libraries, make, X11 (507 kB)
-
The two-body problem (436 kB)
-
The three-body problem and integration of
the Newtonian equations of motion
(4.2 MB)
-
Application ODE: The Lane-Emden equation
(321 kB)
-
Overview: Differential equations, Boundary
value problems
(309 kB)
-
Finding roots, interpolation
(1.1 MB)
-
Numerical Integration and Differentiation
(455 kB)
-
Linear Algebra
(411 KB)
-
Monte-Carlo simulations
(410 kB)
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MC integration, random walks, tests for
randomness (880 kB)
-
Why MC integration, Techniques of
parallelization, OpenMP
(809 kB)
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Insert: data analysis, bootstrapping
(602 kB)
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