Novas funções de forma para o método sem malha de aresta

• Autor(a) principal: Paulo Mariano Inácio da Silva
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/BUOS-ATMKGX
• topic: Campos eletromagnéticos; Espaço H(curl); Métodos numéricos; Método sem malha de aresta; Campos eletromagneticos; Engenharia elétrica; Análise numérica

The Edge Meshless Method is a recently developed numerical method to solve vector boundary value problems. This method uses edge vector shape functions that satisfy the divergence-free condition and thus generate numerical solutions free from spurious modes. Functions are built based on edges instead of nodes, and it assigns degrees of freedom to edges scattered in the domain. The objective of this work is to continue with the development of the Edge Meshless Method, aiming to overcome some of its detected deficiencies. For this, more in-depth studies about the impact of the support edges selection in the solution of electromagnetic problems are carried out and it is proposed a new way to generate vector shape functions for the method. The theory to develop these functions is based on Nédélec's elements of first type in the H(curl; ) space. The mathematical formulation to construct the shape functions is presented and the main characteristics of the method in two dimensions are verfied numerically. It is shown that the numerical solution is not corrupted with spurious modes and that it is possible to generate consistent approximations even when the length of the edgestends to zero.