COMPUTATIONAL ASTROPHYSICS
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Teaching methods
- Contacts/Info
No prerequisites are needed, apart from a basic knowledge of analysis, statistics, and programming in C or Fortran or Python.
The final examination is an oral one. The students will be asked to present one of the topics addressed during the lessons. Then, they will also be asked to choose a science case from the literature, and to critically discuss it.
The goal of the examination is to:
1. verify the proper knowledge of the numerical techniques commonly employed in astrophysics, and their mathematical/physical foundations;
2. assess the ability to critically discuss an actual science case, understand its limitations, and propose alternative approaches.
Computational methods have become crucial in theoretical astrophysics to model complex systems where multiple processes couple non-linearly. This course is aimed at providing students the main capabilities to prepare, perform and analyze numerical simulations of astrophysical systems. We will refer to real science cases developed in the astrophysical literature, yet the discussed methodologies could be of definite interest to anyone involved in any field of modern physics, economy, engineering and social sciences.
At the end of the course students will be able to:
- setup simple numerical simulations of astrophysical systems;
- analyze data outputs of common simulation tools;
- understand how additional physical processes can be included in numerical codes;
- develop massively-parallel codes that can be run on high-performance computing facilities;
- apply big-data techniques to extract statistical information from large simulations.
• Numerical integration of differential equations
• Gravitational dynamics
◦ Introduction to Newtonian and GR dynamics
◦ Gravitational equilibrium: the Poisson-Vlasov equation
◦ N-body effects: relaxation and dynamical friction
◦ Numerical techniques and applications
• Fluid-dynamics
◦ The Navier-Stokes and Euler equations
◦ Riemann problem and approximate solutions
◦ Numerical techniques and applications (e.g. SPH, AMR, moving mesh)
◦ Introduction to magnetohydrodynamics
• Radiation transport: methods and applications
◦ ray-tracing vs momentum-based techniques
◦ Monte Carlo method
• HPC techniques: current status and possible improvements
• Multi-scale simulations: joining resolved and unresolved physical processes
• Big data and exa-scale computing: analysing and post-processing simulations with machine learning and neural networks
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The course is organized in regular frontal lectures with formal introductions followed by real research life examples fully described during the lectures.
For any question, discussion, concern, etc, students are invited to contact the teacher