Funções de forma de ordem superior baseadas em H(curl) para o método sem malha de arest

Abstract

The Edge Meshless Method (EMM) is a numerical method that unlike traditional meshless methods, constructs its approximations based on edges instead of nodes. One of the purposes of this method is to guarantee the condition of the null divergent and to eliminate the spurious modes present in the numerical solution. In this dissertation a mathematical formulation is developed to generate the vector shape functions, so that four, five and six edges can be taken in the support domain. For this, the order of the basic polynomial functions must be increased. The basic functions are based on the H (curl) spaces and in the case of four edges are also based on N´ed´elecs element of first type. The EMM with the new vector shape functions is applied to several electromagnetic problems, for which the permeability and permittivity of the materials are modified. The meshless method can solve these problems satisfactorily, that is, the numerical solution satisfies both the null divergent condition and the continuity of the tangential component of the electric field between two different materia. Besides, the numerical solution does not present spurious modes. The new vector-shape functions generate an increase in the order of convergence when six edges are used in the support domain, because the base function uses a high-order polynomial.