Числовий метод комплексного аналізу ідентифікації параметрів анізотропних середовищ за даними томографії прикладених квазіпотенціалів. Частина 2: Алгоритм та комп’ютерний експеримент

• Date: 2019
• Main Authors: Bomba, Andriy, Boichura, Myhailo
• Format: Article
• Language: English
• Published: Kamianets-Podilskyi National Ivan Ohiienko University 2019
• Online Access: http://mcm-tech.kpnu.edu.ua/article/view/173659
• Journal Title: Mathematical and computer modelling. Series: Technical sciences

An algorithm, which lies in the sequential iterative applying of numerical quasiconformal mapping methods for constructing a series of dynamic meshes using different boundary conditions (that determined by experimental data) and solving the problem of parameter identification for each of these meshes is developed. It is based on the proposed approach to the solving of gradient problems of parameters identification of quasiideal fields with using applied quasipotential tomographic data in cases of anisotropic media and applying the ideas of the block iteration method. The reconstructed image of the distribution of conductivity tensor inside the investigated object, obtained as a result of numerical calculations performed on the basis of the developed algorithm with a sufficient accuracy corresponds to the etalon. The method is characterized by comparatively fast computer convergence (since, unlike many used methods, it does not require finding derivatives of the conductivity tensor distribution function at certain points and refining the boundary nodes at each iteration step). Its significant feature is the possibility of comparatively easy its paralleling and stopping the calculation procedure when some conditions for finishing the process are complete with simultaneous automatic determination the areas of the physical domain where have place large errors of the calculations, which makes it possible to use the machine time more economically. The algorithm for image reconstruction could be extended not only for the medium with a known sum of eigenvalues of the conductivity tensor, but also to cases of other rather wide dependencies between them. In particular, this approach provides an opportunity to represent it as some complex function as required by biomedical practice.