Development and implementation of a well-conditioning approach toward generalized/extended finite element method into an object-oriented platform

• Autor(a) principal: Mohammad Malekan
• Data de Publicação: 2017
• Outros Autores: Felício Bruzzi Barros, Ramon Pereira da Silva
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: https://doi.org/10.26512/ripe.v2i14.21370; http://hdl.handle.net/1843/56906; https://orcid.org/0000-0001-6764-6816
• topic: Generalized/eXtended FEM; Object-oriented programming; Two-scale Analysis; Stable GFEM; Matrix sparsity; Engenharia de estruturas; Controle estrutural (Engenharia)

This paper shows and discusses a generic implementation of the well-conditioning approach toward generalized/extended finite element method. This implementation, performed into an academic computational platform, follows the object-oriented approach presented before for the standard version of GFEM in which the shape functions of finite elements are hierarchically enriched by analytical functions, according to the problem behavior. The stable version of GFEM is employed here to avoid the bad effects of blending elements on the approximate solution convergence rate. Beside this, a sparse matrix data structure is used to accelerate the solution procedure. This approach uses the advantage of sparse matrix to solve the matrix system of equations. The implementations are explained in detail and different aspects of this approach are discussed through numerical examples.