High performance computing for cosmological applications

Period of duration of course
Course info
Number of course hours
Number of hours of lecturers of reference
Number of hours of supplementary teaching

Type of exam



A working knowledge of at least one programming language suitable for scientific computing (e.g. C, fortran, python, julia, etc.) is recommended. Understanding of the cosmic structure formation process is suggested but not mandatory since the needed basic concepts will be introduced during the lectures.


Topic of the course is the study of numerical methods for the solutions of problems in an astrophysical context, in particular focusing on the galaxy formation process on cosmological scales. The course aims at providing a theoretical basis for the numerical integration of the equations of motion for self-gravitating N-body systems, along with the coupling between hydro and radiation dynamics. We will explore different numerical methods and analyze the strengths and limitations of state-of-the-art cosmological simulations techniques. The numerical algorithms will be presented paying close attention to their scalability, cost, and efficiency, in order to be able to exploit high performance computing facilities.

Note that a number of lectures are dedicated to hands-on sessions, in order to develop a practical understanding of the various techniques. Finally, the last few lectures are dedicated to specialized topics, which specific focus will be decided with the attendees.

Educational aims

  1. develop an understanding of the basic theoretical framework needed to set up cosmological and astrophysical problems.
  2. acquire a theoretical and practical knowledge of the numerical methods for gravitational N-body systems and hydrodynamics.
  3. obtain the ability to analyze pros and cons of the techniques used in state-of-the-art works and have a knowledge of current HPC tendencies.

Bibliographical references

Suggested book references are in the following. A list of references for in-depth material/background is also provided. References to specific papers will be given during the lectures.


  •   Hockney, Eastwood                      - Computer simulation using particles (1988, IOP Publishing)
  •   Gnedin, Glover, Klessen, Springel  - Star formation in galaxy evolution: connecting numerical models to reality (2016, Springer)

more on computation:

  •   Aarseth - Gravitational N-body simulations: tools and algorithms (2003, Cambridge University Press)
  •   Press, Teukolsky, Vetterling, Flannery - Numerical recipes: the art of scientific computing (2007, Cambridge University Press)
  •   Toro - Riemann solvers and numerical methods for fluid dynamics: a practical introduction (2009, Springer)

more on physics:

  •   Fasano, Marmi  - Analytical mechanics: an introduction (2006, Oxford University Press)
  •   Chandrasekhar - Hydrodynamic and hydromagnetic stability (1981, Dover)
  •   Sedov              - Similarity and dimensional methods in mechanics (1993, CRC Press)
  •   Padmanabhan   - Structure formation in the Universe (1993, Cambridge University Press)