Name: Abraão Lemos Caldas Frossard
Type: MSc dissertation
Publication date: 02/12/2016

Namesort descending Role
Carlos Friedrich Loeffler Neto Advisor *

Examining board:

Namesort descending Role
Carlos Friedrich Loeffler Neto Advisor *
Guilherme Fabiano Mendonca dos Santos Internal Examiner *
Julio Tomás Aquije Chacaltana External Examiner *
Luciano de Oliveira Castro Lara Co advisor *

Summary: The Boundary Element Method with Direct Integration (DIBEM) has proved to be a
suitable component of the boundary element method to solve problems expressed by
partial differential equations, which have terms that are not given by self-adjoint
operator or require the use of a fundamental solution wich is not related to the
proposed problem. It has been previously used, successfully, in issues governed by
the Poisson and Helmholtz equations. However, every numerical method involves
numerous improvement processes and these aim to enhance the results presented,
adapt it to the solution of a new family problems, decrease its computational cost and
even simplify it mathematically. Seeking to improve the quality of the results
presented by DIBEM, two different expedients for this purpose are tested: first, the
use of different radial basis functions families to analyze what are the functions that
enable to obtain a better accuracy in results; Secondly, the use of an adjustment
scheme of the type proposed by Hadamard to remove the singularity that occurs in
the nucleus of the whole to be interpolated by DIBEM, thus eliminating the need for
separate point sets, one for interpolation and the other for generation of source
points. The evaluation of procedures is made confronting numerical values with the
analytical solution in two-dimensional well-known eigenvalue problems.

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