TITLE: Study of the optimization posibilities of the numerical simulations of some
             physical processes

                   Physics Department, University "Politechnica" Bucharest

ABSTRACT:
 

This study presents the obtained results concerning the optimization possibilities of the: 

a)finite differences(FD) simulations of the ultrasonic pulses propagation in linear attenuative media, 

b) FD simulations of the soliton propagation in KdV media, 

c) random walk simulations of the 1D classical particle diffusion, 

d)gradient method used to evaluate the specific parameters of some physical correlations.

The accomplished studies pointed out that 

a) the FD simulations of the US pulses prpagation through general linear attenuative media are unstable, 

b) the stability and convergence radii depend on the chosen discretization scheme, being very small for the complex wave equation and rather large for the real wave equation, for the classical attenuative Rayleigh-Stokes attenuative media. 

Starting from the well known finding that the FD description of the arbitrary pulse propagation needs their Fourier decomposition this work obtained expressions for: 

i)frequency dependent Zener's effective parameters which allow the description of the monochromatic waves propagation in generalk linear attenuative media as a propagation in a mono-relaxation medium

ii) the frequency dependent Rayleigh-Stokes effective parameters, which allow the FD description of the harmonic components propagation in general attenuative media as a propagation in a classical attenuative medium with rather high stability and convergence radii.

The similar study of the pulses propagation through Korteweg-de Vries media pointed out that 

i) the accuracy of the FD simulations improves considerably when the time step increases (for given values of the space step and of the characteristic pulse parameters) towards the Vliegenhart's threshold,

 ii) the FD simulations instability appears suddenly for values of the time step somewhat less than the predicted Vliegenhart's threshold, 

iii) the non-solitonic pulses spread during the propagation in a KdV medium in several solitons.

The accoplished study of the binomial and trinomial random walk simulations of the 1D diffusion and drift of classical particles pointed out: a) the convergence of both simulation towards the true evolution for sufficiently high values of the number of time steps. The binomial and trinomial simulations are located in opposite sides of the true distribution but the trinomila simulations is approximately twice nearer to the Fokker-Planck plot than the binomial distribution.

Similarly, the study of the search gradient method pointed out: 

i) the importance of the proper choice of the uniqueness parameters and of their zero order approximation values, ii) the usefulness of the suitably chosen damping of the components of the gradient correction vector in each iteration, 

iii)the very quick convergence of the improved version of the gradient method and its efficiency measured in apparent and real true information amounts/iteration for the thermally stimulated depolarization currents experimental data.

back