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

algorithmIn mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

s to solve problems in

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

for which a quantitative theory already exists. It is often regarded as a subdiscipline of

theoretical physicsTheoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...

but some consider it an intermediate branch between theoretical and

experimental physicsWithin the field of physics, experimental physics is the category of disciplines and sub-disciplines concerned with the observation of physical phenomena in order to gather data about the universe...

.

PhysicistA physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

s often have a very precise mathematical theory describing how a system will behave. Unfortunately, it is often the case that solving the theory's equations

ab initioab initio is a Latin term used in English, meaning from the beginning.ab initio may also refer to:* Ab Initio , a leading ETL Tool Software Company in the field of Data Warehousing.* ab initio quantum chemistry methods...

in order to produce a useful prediction is not practical. This is especially true with

quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, where only a handful of simple models admit closed-form, analytic solutions. In cases where the equations can only be solved approximately, computational methods are often used.

## Applications of computational physics

Computation now represents an essential component of modern research in

accelerator physicsAccelerator physics deals with the problems of building and operating particle accelerators.The experiments conducted with particle accelerators are not regarded as part of accelerator physics. These belong to particle physics, nuclear physics, condensed matter physics, materials physics, etc...

,

astrophysicsAstrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...

,

fluid mechanicsFluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...

,

lattice field theoryIn physics, lattice field theory is the study of lattice models of quantum field theory, that is, of field theory on a spacetime that has been discretized onto a lattice. Although most lattice field theories are not exactly solvable, they are of tremendous appeal because they can be studied by...

/

lattice gauge theoryIn physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important in particle physics, and include the prevailing theories of elementary particles: quantum electrodynamics, quantum chromodynamics and the Standard...

(especially

lattice quantum chromodynamicsLattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time....

), plasma physics (see

plasma modelingPlasma Modeling refers to solving equations of motion that describe the state of a plasma. It is generally coupled with Maxwell's Equations for electromagnetic fields...

), solid state physics and soft condensed matter physics. Computational solid state physics, for example, uses

density functional theoryDensity functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by...

to calculate properties of solids, a method similar to that used by chemists to study molecules.

As these topics are explored, many more general numerical and

mathematicalMathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

problems are encountered in the process of calculating physical properties of the modeled systems. These include, but are not limited to

- Solving differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

s
- Evaluating integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...

s
- Stochastic methods, especially Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...

s
- Specialized partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

methods, for example the finite differenceA finite difference is a mathematical expression of the form f − f. If a finite difference is divided by b − a, one gets a difference quotient...

method and the finite element methodThe finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...

- The matrix eigenvalue problem – the problem of finding eigenvalues of very large matrices, and their corresponding eigenvectors (eigenstates in quantum physics)
- The pseudo-spectral method
Pseudo-spectral methods are a class of numerical methods used in applied mathematics and scientific computing for the solution of PDEs, such as the direct simulation of a particle with an arbitrary wavefunction interacting with an arbitrary potential...

Computational physics also encompasses the tuning of the software/hardware structure to solve problems. Approaches to solving the problems are often very demanding in terms of processing power and/or memory requests.

## See also

- Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...

- Computational fluid dynamics
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...

- Computational Magnetohydrodynamics
Computational magnetohydrodynamics is a rapidly developing branch of magnetohydrodynamics that uses numerical methods and algorithms to solve and analyze problems that involve electrically conducting fluids. Most of the methods used in CMHD are borrowed from the well established techniques...

- DCOMP Division of Computational Physics of the American Physical Society
- Important publications in computational physics
- Computational Science
- Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...

- Open Source Physics
Open Source Physics, or OSP, is a project sponsored by the National Science Foundation and Davidson College, whose mission is to spread the use of open source code libraries, tools, and compiled simulations for physics and other numerical simulations. The OSP collection provides curriculum...

, computational physics libraries and pedagogical tools
- Plasma modeling
Plasma Modeling refers to solving equations of motion that describe the state of a plasma. It is generally coupled with Maxwell's Equations for electromagnetic fields...

## External links