Methods of Computational Physics 1

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Laser Physics and Photonics

Synopsis:

Numerical simulation and its role in physics, methodology of writing computer codes. Numerical and programming techniques for simulations of physics problems. Computer languages for physics. Numerical libraries and program libraries for physics. Computer tools for scientific visualization. Simulations of continuous systems, hydrodynamic simulations. High-performance computing, parallel computing, software for parallel simulations. Integrated computing environments.

Requirements:

Syllabus of lectures:

1. Computers in physics. Computer experiment. Laws of physics, mathematical models, numerical scheme.

2. Computer hardware, computer memory hierarchy. Supercomputers, high-performance computing. Computer languages for physics, compilers. Numerical libraries.

3. Scientific databases. Electronic databases of scientific journals and reports. Evaluation of scientific journals and scientists, publications, citation analysis.

4. Parallel computing, shared/distributed memory computing. Software tools and libraries for parallelization.

5. Methodology of scientific programming. Errors in scientific codes. Numerical algorithms for physics.

6. Scientific visualization. Types of graphs in physics. Software tools for scientific visualization.

7. Computational fluid dynamics (CFD). Experiment versus simulation. Euler equations. Computational meshes, discretization in time and space. Verification and validation. Software tools for CFD.

8. Finite elements - finite differences, difference schemes, explicit/implicit schemes.

9. Finite volumes - integral form of the equations, numerical methods for integration.

10. Finite elements - approximation by basis functions, reduction of PDE by a system of ODEs.

11. Spectral methods, boundary elements methods, mesh-free methods, smoothed-particle hydrodynamics.

12. Staggered Lagrangian hydrodynamics - derivation and conservation. Arbitrary Lagrangian-Eulerian methods - mesh regularization, remap. Applications for simulations of laser-plasma interactions.

13. Integrated computing systems - computer algebra, numerics, visualization. Available systems.

Syllabus of tutorials:

1. Transformation of a physics problem to a numerical code.

2. Paralel code for shared/distributed memory.

3. Example of visualization in selected software tools.

4. Example of selected integrated computing systems.

Study Objective:

Knowledge:

Acquiring the overview of methods and computer tools for designing, analysis, solving, and visualization of physics problems. Knowledge of methods for computational fluid dynamics.

Skills:

Ability to prepare a short presentation on a given physics-related topic. Ability to understand a simple numerical code.

Study materials:

Key references:

[1] R.H. Landau, M.J. Páez, Ch.C. Bordeianu: A Survey of Computational Physics - Introduction to Computational Sciences, Princeton University Press, 2008.

Recommended references:

[2] H. Gould, J. Tobochnik, W. Christian: An Introduction to Computer Simulation Methods - Applications to Physical Systems, 3rd edition, Pearson, 2007.

[3] T. Pang: An Introduction to Computational Physics, Cambridge University Press, 1997.

Others:

UNIX computer laboratory.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• BS Informatická fyzika (compulsory course of the specialization)