**Computational physics** is the study and implementation of numerical analysis 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 .

It is sometimes considered a subdiscipline (or offshoot) of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics , a third way that supplements theory and experiment. ^{[2]}

## Overview

^{[3]}

In physics, different theories based on mathematical models provide very accurate predictions on how systems behave. Unfortunately, it is often the case that the mathematical model for a particular system 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 thesis numerical approximations: the approximation of the solution is written as a finite (and wide Typically) number of single mathematical operations ( algorithm ), and a computer is used to perform thesis operations and compute year Approximated solution and respectiveerror . ^{[1]}

### Status in physics

There is a debate about the status of computation within the scientific method. ^{[4]}

Sometimes it is considered to be akin to theoretical physics; some others others computer simulation as ” computer experiments “, ^{[4] and} still others consider it an intermediate or different branch between theoretical and experimental physics , a third way that supplements theory and experiment. While computers can be used for measuring and recording data, this clearly does not constitute a computational approach.

## Challenges in computational physics

Physics problems are in general very difficult to solve exactly. This is due to several (mathematical) reasons: lack of algebraic and / or analytic solubility, complexity , and chaos.

For example, – even apparently simple problems, such as calculating the wavefunction of an electron orbiting an atom in a strong electric field ( Stark effect ), may require great effort to formulate a practical algorithm (if one can be found); other cruder gold brute-force techniques, such as graphical methods or root finding , may be required. On the more advanced side, mathematical perturbation theory est Sometimes used (a working is shown for this Particular example here ).

In addition, the computational cost and computational complexity for many-body problems (and their classical counterparts ) tends to grow quickly. A macroscopic system typically has a size of the order of23constitute particles, so it is somewhat of a problem. Solving quantum mechanical problems Generally is of exponential order in the size of the system ^{[ citation needed ]} and for classical N-body it is of order N-squared.

Finally, Many physical systems are inherently nonlinear at best, and at worst chaotic : this means clustering it can be difficulty to Ensure Any numerical errors do not grow to the point of rendering the ‘solution’ useless. ^{[5]}

## Methods and algorithms

Because computational physics uses a broad class of problems, it is generally divided between different mathematical problems. Between them, one can consider:

- root finding (using eg Newton-Raphson method )
- system of linear equations (using eg LU decomposition )
- ordinary differential equations (using eg Runge-Kutta methods )
- integration (using eg Romberg and Monte Carlo integration )
- Partial Differential Equations (using the finite difference method and relaxation method)
- matrix eigenvalue problem (using eg Jacobi eigenvalue algorithm and power iteration )

All these methods (and several others) are used to calculate the properties of the modeled systems.

Computational computational physics computational computational computational chemistry – for example, computational solid state computational solid state computational physicists to calculate properties of solvents.

Further, computational physics encompasses the tuning of the software / hardware structure to solve the problems (as the problems usually can be very large, in processing power need or in memory requests ).

## Divisions

It is possible to find a corresponding computational branch for every major field in physics, for example computational mechanics and computational electrodynamics . Computational mechanics consists of computational fluid dynamics (CFD), computational solid mechanics, and computational contact mechanics . One subfield at the confluence between CFD and electromagnetic modeling is computational magnetohydrodynamics . The quantum many-body problem leads naturally to the large and rapidly growing field of computational chemistry .

Computational Solid State Physics is a very important division of computational physics dealing directly with material science.

A field related to computational condensed matter is computational statistical mechanics, qui deals with the simulation of models and theories (Such As percolation and spin models ) That are difficulties to solve Otherwise. Computational statistical physics makes heavy use of Monte Carlo-like methods. More Broadly, (PARTICULARLY through the use of agent based modeling and cellular automata ) it aussi Concerns Itself with (and finds implementation in, through the use of ict technical) in the social sciences, network theory, and mathematical models for the spread of disease (most notably, the SIR Model ) and the spread of forest fires .

On the more esoteric side, numerical relativity is a (Relatively) new field interested in finding solutions to the numeric field equations of general (and special) relativity, and computational particle physics deals with problems motivated by particle physics.

Computational astrophysics is the application of these techniques and methods to astrophysical problems and phenomena.

## Applications

Due to the broad class of problems computational physics deals, it is an essential component of modern research in different areas of physics derived, namely: accelerator physics , astrophysics , fluid mechanics ( computational fluid dynamics ), lattice field theory / lattice gauge theory (especially lattice quantum chromodynamics ), plasma physics (see plasma modeling ) simulating physical systems (using eg molecular dynamics ), protein structure prediction , weather prediction , solid State physics ,soft condensed matter physics, hypervelocity impact physics etc.

Computational Solid State Physics, for example, uses density functional theory to calculate properties of solids, a method similar to That Used by chemists to study molecules. Other quantities of interest in solid state physics, Such As the electronic band structure, magnetic properties and load densified Can Be Calculated by this and several methods, Including the Luttinger-Kohn / kp method and ab initio methods.

## See also

- Advanced Simulation Library
- CECAM – European Center for Atomic and Molecular Computing
- Division of Computational Physics (DCOMP) of the American Physical Society
- Important publications in computational physics
- Mathematical and theoretical physics
- Open Source Physics , computational physics libraries and pedagogical tools
- Timeline of computational physics

## References

- ^ Jump up to:
^{a}Thijssen^{b}, Joseph (2007).*Computational Physics*. Cambridge University Press . ISBN 0521833469 . **Jump up^**Landau, Rubin H .; Páez, Manuel J .; Bordeianu, Cristian C. (2015).*Computational Physics: Problem Solving with Python*. John Wiley & Sons .**Jump up^**Landau, Rubin H .; Paez, Jose; Bordeianu, Cristian C. (2011).*A survey of computational physics: introductory computational science*. Princeton University Press .- ^ Jump up to:
^{a }^{b}molecular dynamics primer , Furio Ercolessi, University of Udine , Italy. Article PDF . **Jump up^**“How Long Does Numerical Chaotic Solutions Remain Valid?”. Bibcode : 1997PhRvL..79 … 59S . doi : 10.1103 / PhysRevLett.79.59 .