Name: Áquila de Jesus dos Santos
Type: MSc dissertation
Publication date: 06/05/2021
Advisor:

Namesort descending Role
Carlos Friedrich Loeffler Neto Advisor *

Examining board:

Namesort descending Role
Andre Bulcão External Examiner *
Carlos Friedrich Loeffler Neto Advisor *
José Antonio Fontes Santiago External Examiner *
Lucas Silveira Campos External Examiner *
Luciano de Oliveira Castro Lara Internal Examiner *

Summary: In this work, the influence of numerical integration on the precision of the Boundary Element Method (MEC) is analyzed when it is applied to two-dimensional field problems, using linear, quadratic and cubic isoparametric elements. For high-order elements (quadratic and cubic, in this work), unlike the constant and linear elements, the modus operandi of the coordinate transformations, the numerical integration procedures, and the treatment of singular integrals is not simple, since the Jacobian of transformation is no longer constant across the element and needs to be treated numerically. In this sense, the evaluation of the impact of the self-adaptive integration scheme in the solution of integrals of MEC has a special emphasis in this work.
Examples of scalar field problems associated with the Laplace and Advection-Diffusion equations, and Autovalor problems, associated with the Helmholtz equation are solved using the standard Gaussian integration and the self-adaptive integration scheme. Then, their results are compared with the analytical or numerical solutions already validated to evaluate the numerical efficiency.

Key words: Laplace’s Equation; Diffusive-Advective Equation; Helmholtz Equation; Numerical integration; Gaussian Quadrature.

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