computational physics this article is about computational science applied in physics for theories comparing the universe to a computer see digital physics for the study of the fundamental physical limits of computers see physics of computation computational physics numerical analysis simulation data analysis visualization potentialsmorselongrange potential lennardjones potential yukawa potential morse potential fluid dynamicsfinite difference finite volume finite element boundary element lattice boltzmann riemann solver dissipative particle dynamics smoothed particle hydrodynamics turbulence models monte carlo methodsintegration gibbs sampling metropolis algorithm particlenbody particleincell molecular dynamics scientistsgodunov ulam von neumann galerkin lorenz wilson vte computational physics is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists historically computational physics was the first application of modern computers in science and is now a subset of computational science it is sometimes regarded as 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 overview a representation of the multidisciplinary nature of computational physics both as an overlap of physics applied mathematics and computer science and as a bridge among them 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 closedform 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 status in physics there is a debate about the status of computation within the scientific method sometimes it is regarded as more akin to theoretical physics some others regard computer simulation as computer experiments yet 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 in experiments for the measurement and recording and storage of 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 andor 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 or bruteforce techniques such as graphical methods or root finding may be required on the more advanced side mathematical perturbation theory is also sometimes used a working is shown for this particular example here in addition the computational cost and computational complexity for manybody problems and their classical counterparts tend to grow quickly a macroscopic system typically has a size of the order of 10 23 displaystyle 1023 constituent particles so it is somewhat of a problem solving quantum mechanical problems is generally of exponential order in the size of the system and for classical nbody it is of order nsquared finally many physical systems are inherently nonlinear at best and at worst chaotic this means it can be difficult to ensure any numerical errors do not grow to the point of rendering the solution useless methods and algorithms because computational physics uses 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 root finding using eg newtonraphson method system of linear equations using eg lu decomposition ordinary differential equations using eg rungekutta methods integration using eg romberg method and monte carlo integration partial differential equations using eg 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 physical properties of the modeled systems computational physics also borrows a number of ideas from computational chemistry for example the density functional theory used by computational solid state physicists to calculate properties of solids is basically the same as that used by chemists to calculate the properties of molecules furthermore computational physics encompasses the tuning of the softwarehardware 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 modelling is computational magnetohydrodynamics the quantum manybody 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 which deals with the simulation of models and theories such as percolation and spin models that are difficult to solve otherwise computational statistical physics makes heavy use of monte carlolike methods more broadly particularly through the use of agent based modeling and cellular automata it also concerns itself with and finds application in through the use of its techniques in the social sciences network theory and mathematical models for the propagation 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 numeric solutions to the 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 computational biophysics is a branch of biophysics and computational biology itself applying methods of computer science and physics to large complex biological problems 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 theorylattice gauge theory especially lattice quantum chromodynamics plasma physics see plasma modeling simulating physical systems using eg molecular dynamics nuclear engineering computer codes 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 charge densities can be calculated by this and several methods including the luttingerkohnkp method and abinitio methods advanced simulation library cecam centre europen de calcul atomique et molculaire 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 ak 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 addisonwesley 1986 t pang an introduction to computational physics cambridge university press 2010 b stickler e schachinger basic concepts in computational physics springer verlag 2013 isbn9783319024349 e winsberg science in the age of computer simulation chicago university of chicago press 2010 wikimedia commons has media related to computational physics c20 iupap commission on computational physics applied physical society division of computational physics institute of physics computational physics group scidac scientific discovery through advanced computing open source physics scinet scientific software framework vtebranches of physicsdivisions theoretical phenomenology computational experimental applied classicalclassical mechanics acoustics ballistics continuum fluid solid hamiltonian lagrangian electrodynamics electrostatics magnetostatics plasma physics statistical mechanics thermodynamics condensed matter materials mesoscopic polymers soft solidstate moderncosmology astrophysics nuclear celestial mechanics solar heliophysics space physics relativity general special particle physics accelerator astroparticle nuclear quantum chromodynamics quantum mechanics quantum electrodynamics quantum field theory quantum gravity atomic molecularand optical physics atomic physics molecular physics optics photonics quantum optics interdisciplinary agrophysics biophysics medical neurophysics engineering geophysics atmospheric cloud mathematical physical chemistry chemical physics quantum computing social physics econophysics see also history of physics nobel prize in physics timeline of physics discoveries theory of everything vtemajor fields of computer sciencenote this template roughly follows the 2012 acm computing classification systemhardware printed circuit board peripheral integrated circuit very large scale integration systems on chip socs energy consumption green computing electronic design automation hardware acceleration computer systemsorganization computer architecture embedded system realtime computing dependability networks network architecture network protocol network components network scheduler network performance evaluation network service software organization interpreter middleware virtual machine operating system software quality software notationsand tools programming paradigm programming language compiler domainspecific language modeling language software framework integrated development environment software configuration management software library software repository software development software development process requirements analysis software design software construction software deployment software maintenance programming team opensource model theory of computation model of computation formal language automata theory computational complexity theory logic semantics algorithms algorithm design analysis of algorithms algorithmic efficiency randomized algorithm computational geometry mathematicsof computing discrete mathematics probability statistics mathematical software information theory mathematical analysis numerical analysis informationsystems database management system information storage systems enterprise information system social information systems geographic information system decision support system process control system multimedia information system data mining digital library computing platform digital marketing world wide web information retrieval security cryptography formal methods security services intrusion detection system hardware security network security information security application security humancomputerinteraction interaction design social computing ubiquitous computing visualization accessibility concurrency concurrent computing parallel computing distributed computing multithreading multiprocessing artificialintelligence natural language processing knowledge representation and reasoning computer vision automated planning and scheduling search methodology control method philosophy of artificial intelligence distributed artificial intelligence machine learning supervised learning unsupervised learning reinforcement learning multitask learning crossvalidation graphics animation rendering image manipulation graphics processing unit mixed reality virtual reality image compression solid modeling appliedcomputing ecommerce enterprise software computational mathematics computational physics computational chemistry computational biology computational social science computational engineering computational healthcare digital art electronic publishing cyberwarfare electronic voting video games word processing operations research educational technology document management book category portal wikiproject commons 