Estudo do desempenho do Método dos Elementos de Contorno utilizando esquema de integração autoadaptativo em problemas de campo escalar bidimensionais

Abstract

This work analyzes the influence of numerical integration on the accuracy of the Boundary Element Method (BEM) when applied to two-dimensional field problems, using linear, quadratic and cubic isoparametric elements. For high-order elements, unlike constant and linear elements, the modus operandi of coordinate transformations, numerical integration procedures and the treatment of singular integrals are not simple, since the Jacobian The transformation is no longer constant throughout the element and need to be handled numerically. In this sense, the evaluation of the impact of the self-adaptive integration scheme in the solution of integrals in the BEM has a special emphasis in this work. Examples of scalar field problems, associated with Laplace and Advection-Diffusion equations, and Eigenvalue problems, associated with Helmholtz equation, are solved using the classical Gaussian Quadrature (Gauss-Legendre) and the self-adaptive integration scheme in the solution of integrals in the BEM has a special emphasis in this work. Examples of scalar field problems, associated with Laplace and Advection-Diffusion equations, and Eigenvalue problems, associated with Helmholtz equation, are solved using the classical Gaussian Quadrature (Gauss-Legendre) and the self-adaptive integration scheme proposed by (TELLES, 1987). Then, their results are compared with validated analytical or numerical solutions to assess numerical efficiency scheme proposed by (TELLES, 1987). Then, their results are compared with validated analytical or numerical solutions to assess numerical efficiency.