Analisi e Applicazione di Funzioni a Base Radiale Anisotropiche

When a person is intubated, forced induced breathing causes injuries to the diaphragm. The purpose of the INVIVE project is to create a simulation of the ribcage in order to study the movement of the diaphragm to prevent damage. In this thesis, we analyze approximations of certain functions obtained using kernels on a semi-annular domain representing the diaphragm. In the first chapter we give definitions of isotropic and anisotropic radial-based functions and use them to find solutions to an interpolation problem. The second address the radial-based unit partitioning method. The following defines the equations to elliptical partial derivatives and presents possible methods for obtaining solutions. The fourth chapter is the first purely application in which you search for the shape parameter that optimizes the interpolation of types of functions on the domain. Solutions obtained with isotropic and anisotropic radial-based functions are compared using RMS error, maximum error, and computational cost as indicators. The following chapter seeks the solution of an elliptical PDE always defined on the semi-ring: 3 variants of the Kansa method are presented. These are observed if they give accurate approximations and in the case of search for the optimal value of the radial-based function shape parameter. In these last two chapters there is a section that shows the MATLAB codes used.