Avaliação do desempenho de técnicas para melhoria da formulação MECID em problemas de autovalor

Abstract

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 governedby 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