Cálculo de derivadas espaciais através de interpolação com funções de base radial no contexto do método dos elementos de contorno

Abstract

Initially applied in the context of the Boundary Element Method as an auxiliary tool, interpolating the core of domain integrals and allowing their transformation into boundary integrals, the radial basis functions have expanded their field of application and are currently widely used as a technique. solution of partial differential equations, generating the so-called meshless formulations of the Finite Element Method. Recently, they have also been shown to be a numerical tool for the simpler calculation of spatial derivatives. Naturally, in these cases there is a loss of precision related to interpolation; but even so, its use can be advantageous due to the complexity of certain techniques involving the analytical derivation of primal variables and other more classical procedures, especially within the Boundary Element Method. In this sense, this work evaluates a series of characteristics peculiar to the derivation procedure with radial basis functions, such as the influence of the dimensions of the problem on the results, the effect of the contour refinement, the effect of the internal consolidation of interpolating points and the variations in the accuracy due to the type of radial basis function used. To evaluate such characteristics, this dissertation simulates three two-dimensional test problems that have a known analytical solution, performing the necessary performance comparisons and reaching some important conclusions regarding its applicability.