Finite-difference method for solution to general boundary problem of hyperbolic-type equation in multi-layer domain

Аuthors

Alifanov O. M.^1*, Nenarokomov A. V.^2**, Nenarokomov K. A.¹, Terent'eva A. V.^1***, Titov D. M.^1****

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. ,

*e-mail: o.alifanov@yandex.ru
**e-mail: nenarokomovav@mai.ru
***e-mail: tav-21@mail.ru
****e-mail: d.titov@mai.ru

Abstract

Basic principles and architecture are considered for the problem-oriented program package for solving non- linear ill-posed inverse problems for hyperbolic equation in one-dimensional non-stationary statement. Computational algorithms will be realized in the package for solution to inverse problems and will be built by using the iterative regularization method. The program package will have a multi-level modular structure. The developed algorithm make possible taking into account all keeping experimental information for estimation of materials properties.
The equations for calculations of the wave propagation which provide estimation of material properties were formulated. Some ways are suggested for local elements representation. It allows to include the simulating programs in global program to solve the inverse problems for identifying effective characteristics of elastic materials. In the framework of this approach a general direct model were developed:


where L is number of layers in the system. The Finite Difference algorithm has been developed as basic approach for simulation of 1-D wave propagation in composite materials. The special uniform Finite Difference approximation was developed for multi-layer domain with different properties of materials.

Keywords:

wave prorogation, finite differences, nonlinear acoustics, inverse problems, numerical method

References

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2. Formalev V.F., Reviznikov D.L. Chislennye metody (Numerical methods), Moscow, FIZMATLIT, 2006, 400 p.