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Computational physics
 
 
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Computational physics is the study and implementation of numerical algorithm
Algorithm

In mathematics, computing, linguistics and related subjects, an algorithm is a sequence of finite instructions, often used for calculation and data processing....
s in order to solve problems in physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
 for which a quantitative theory already exists. It is often regarded as a subdiscipline of theoretical physics
Theoretical physics

Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain experimental data taken of the natural world....
 but some consider it an intermediate branch between theoretical and experimental physics
Experimental physics

Within 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....
.

Physicist
Physicist

A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many Physics#Major fields of physics spanning all length scales: from atom 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 initio
Ab initio

The Latin term ab initio means from the beginning and is used in several contexts:* when describing literature: told from the beginning as opposed to in medias res ...
 in order to produce a useful prediction is not practical.






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Computational physics is the study and implementation of numerical algorithm
Algorithm

In mathematics, computing, linguistics and related subjects, an algorithm is a sequence of finite instructions, often used for calculation and data processing....
s in order to solve problems in physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
 for which a quantitative theory already exists. It is often regarded as a subdiscipline of theoretical physics
Theoretical physics

Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain experimental data taken of the natural world....
 but some consider it an intermediate branch between theoretical and experimental physics
Experimental physics

Within 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....
.

Physicist
Physicist

A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many Physics#Major fields of physics spanning all length scales: from atom 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 initio
Ab initio

The Latin term ab initio means from the beginning and is used in several contexts:* when describing literature: told from the beginning as opposed to in medias res ...
 in order to produce a useful prediction is not practical. This is especially true with quantum mechanics
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
, where only a handful of simple models have complete analytic solutions. In cases where the systems only have numerical solutions, computational methods are used.

Applications of computational physics

Computation now represents an essential component of modern research in accelerator physics
Accelerator physics

Accelerator 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....
, astrophysics
Astrophysics

Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of astronomical objects such as galaxy, stars, planets, exoplanets, and the interstellar medium, as well as their interactions....
, fluid mechanics
Fluid mechanics

Fluid mechanics is the study of how fluids move and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest, and fluid dynamics, the study of fluids in motion....
, lattice field theory
Lattice field theory

In physics, lattice field theory is the study of lattice model of quantum field theory, that is, of field theory on a spacetime that has been discretized onto a lattice ....
/lattice gauge theory
Lattice gauge theory

In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized onto a lattice . Although most lattice gauge theories are not exactly solvable, they are of tremendous appeal because they can be studied by simulation on a computer....
 (especially lattice quantum chromodynamics
Lattice QCD

In physics, lattice quantum chromodynamics is a theory of quarks and gluons formulated on a space-time lattice . That is, it is a lattice model of quantum chromodynamics, a special case of a lattice gauge theory or lattice field theory....
), plasma physics (see plasma modeling
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 ....
) and solid state physics. Computational solid state physics, for example, uses density functional theory
Density functional theory

Density functional theory is a quantum mechanics theory used in physics and chemistry to investigate the electronic structure of Many-body problem, in particular atoms, molecules, and the condensed phases....
 to calculate properties of solids, a method similar to that used by chemists to study molecules.

Many other more general numerical problems fall loosely under the domain of computational physics, although they could easily be considered pure mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 or part of any number of applied areas. These include

  • Solving differential equation
    Differential equation

    A differential equation is a mathematics equation for an unknown function of one or several variable that relates the values of the function itself and its derivatives of various orders....
    s
  • Evaluating integral
    Integral

    Integration is an important concept in mathematics, specifically in the field of calculus and, more broadly, mathematical analysis. Given a function ƒ of a Real number variable x and an interval [a, b] of the real line, the integral...
    s
  • Stochastic methods, especially Monte Carlo method
    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 when computer simulation physics and mathematics systems....
    s
  • Specialized partial differential equation
    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 its partial derivatives with respect to those variables....
     methods, for example the finite difference
    Finite difference

    A 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 method
    Finite element method

    The finite element method is a numerical analysis for finding approximate solutions of partial differential equations as well as of 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 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 energy....


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

See also

  • Molecular dynamics
    Molecular dynamics

    Molecular dynamics is a form of computer simulation in which atoms and molecules are allowed to interact for a period of time by approximations of known physics,...
  • Computational fluid dynamics
    Computational fluid dynamics

    Computational fluid dynamics is one of the branches of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows....
  • Computational Magnetohydrodynamics
    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....
  • Important publications in computational physics
    List of publications in physics

    Optics...
  • Computational Science
  • Mathematical physics
    Mathematical physics

    Mathematical physics is the scientific discipline concerned with the interface of mathematics and physics. There is no real consensus about what does or does not constitute mathematical physics....
  • Plasma modeling
    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 ....


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