Computational physics

Computational physics
Numerical analysis · Simulation Data analysis · Visualization
Potentials Lennard-Jones potential · Yukawa potential · Morse potential
Fluid dynamics Finite element · Riemann solver Smoothed particle hydrodynamics
Monte Carlo methods Integration · Gibbs sampling · Metropolis algorithm
Particle N-body · Particle-in-cell Molecular dynamics
Scientists Godunov · Ulam  · von Neumann

Computational physics is the study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists^[1]. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science^[2].

Overview

In Physics, different theories based on mathematical models provide very precise predictions on how systems behave. Unfortunately, it is often the case that solving the mathematical model for a particular system in order to produce a useful prediction is not feasible. This can occur, for instance, when the solution does not have a closed-form expression, or is too complicated. In such cases, numerical approximations are required. Computational physics is the subject that deals with these numerical approximations: the approximation of the solution is written as a finite (and typically large) number of simple mathematical operations (algorithm), and a computer is used to perform these operations and compute an approximated solution and respective error^[1].

Methods and Algorithms

Because computational physics is used in a broad class of problems, it is generally divided amongst the different mathematical problems it numerically solves, or the methods it applies. Between them, one can consider:

• Ordinary differential equations (using e.g. Runge–Kutta methods)
• integration (using numerical integration or Monte Carlo integration)
• partial differential equations, for example the finite difference method, the finite element method or pseudo-spectral method
• The matrix eigenvalue problem - finding eigenvalues and their corresponding eigenvectors of very large matrices, (which correspond to eigenenergies and eigenstates in quantum physics)
• simulating physical systems (using e.g. Molecular dynamics)
• Protein structure prediction

Applications

Due to the broad class of problems computational physics deals, it is an essential component of modern research in different areas of physics, namely: accelerator physics, astrophysics, fluid mechanics (computational fluid dynamics), lattice field theory/lattice gauge theory (especially lattice quantum chromodynamics), plasma physics (see plasma modeling), solid state physics, soft condensed matter physics, etc.

See also

• Important publications in computational physics
• Computational magnetohydrodynamics
• Division of Computational Physics (DCOMP) of the American Physical Society
• CECAM - Centre européen de calcul atomique et moléculaire
• Mathematical physics
• Open Source Physics, computational physics libraries and pedagogical tools

References

Other references

• A.K. Hartmann, Practical Guide to Computer Simulations, World Scientific (2009)
• International Journal of Modern Physics C (IJMPC): Physics and Computers, World Scientific
• Steven E. Koonin, Computational Physics, Addison-Wesley (1986)
• R.H. Landau, C.C. Bordeianu, and M. Jose Paez, A Survey of Computational Physics: Introductory Computational Science, Princeton University Press (2008)
• T. Pang, An Introduction to Computational Physics, Cambridge University Press (2010)
• J. Thijssen, Computational Physics, Cambridge University Press (2007)

External links

• C20 IUPAP Commission on Computational Physics
• APS DCOMP
• IoP CPG (UK)
• SciDAC: Scientific Discovery through Advanced Computing
• Open Source Physics
• SCINET Scientific Software Framework