New Algorithm For Numerical Simulation Research Articles

Accounting for the effect of large-scale atmospheric inhomogeneities in problems of laser radiation propagation along long high-altitude paths

We show that large-scale atmospheric inhomogeneities observed experimentally can significantly affect optical radiation propagation along long paths, and it is impossible to take into account this effect within the classical turbulence model. We suggest a new algorithm for numerical simulation of laser beam propagation along long low-inclined atmospheric paths with large-scale atmospheric inhomogeneities, which allows one to consider beam refraction and focusing at large-scale inhomogeneities along with beam distortions due to small-scale inhomogeneities and regular refraction in a vertical plane.

Numerical simulation of laser welding of thin metallic plates taking into account convection in the welding pool

A new algorithm for numerical simulation of laser welding of thin metallic plates was developed here. It is based on the collocations and least squares method and a new quasi-three-dimensional model of laser welding process. Calculations for titanium plates were carried out. An influence of the convection on the welding process was investigated.

New algorithm for numerical simulation of the propagation of laser radiation

A new more accurate calculation algorithm (with a variable grid-mesh size) is proposed for the propagation of radiation considered in the paraxial approximation based on the Fresnel — Kirchhoff formula. The algorithm was used to develop the FRESNEL program intended for simulation of the propagation of radiation through laser systems. Examples of calculations carried out with the new algorithm are given and they are compared with the traditional method.

A new algorithm for numerical simulation of Langevin equations

Formulated is a new systematic method for obtaining higher order corrections in numerical simulation of stochastic differential equations (SDEs), i.e., Langevin equations. Random walk step algorithms within a given order of finite Δt, are obtained so as to reproduce within that order a corresponding transition density of the Fokker-Planck equations, in the weak Taylor approximation scheme [1]. A great advantage of our method is its straightforwardness such that direct perturbative calculations produce the algorithm as an end result, so that the procedure is tractable by computer. Examples in general form for curved space cases as well as flat space cases are given in some order of approximations. Simulations are performed for specific examples of U(1) system and SU(2) systems, respectively.