Computational physics
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Numerical analysis · Simulation
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Computational physics is the study and implementation of numerical algorithms in order to solve problems in physics for which a quantitative theory already exists. It is often regarded as a subdiscipline of theoretical physics but some consider it an intermediate branch between theoretical and experimental physics.
Physicists 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 in order to produce a useful prediction is not practical. This is especially true with quantum mechanics, where only a handful of simple models have complete analytic solutions. In cases where the systems only have numerical solutions, computational methods are used.
[edit] Applications of computational physics
Computational methods are widely used in solid state physics, fluid mechanics, and lattice field theory/lattice gauge theory (especially lattice quantum chromodynamics), among other areas. 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. In solid state physics, the electronic band structure, magnetic properties and charge densities can be calculated by several methods, including the Luttinger-Kohn k.p method and ab initio methods.
Many other more general numerical problems fall loosely under the domain of computational physics, although they could easily be considered pure mathematics or part of any number of applied areas. These include
- Solving differential equations
- Evaluating integrals
- Stochastic methods, especially Monte Carlo methods
- Specialized partial differential equation methods, for example the finite difference method and the finite element method
- 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
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).
