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COBEM 2017
24th ABCM International Congress of Mechanical Engineering
COMPARISON OF EIGENPROBLEM SOLUTION APPROACHES FOR DIRICHLET CONDITIONS IN IRREGULAR DOMAINS VIA INTEGRAL TRANSFORMS
Submission Author:
Isabela Florindo Pinheiro , RJ
Co-Authors:
Leandro Alcoforado Sphaier, Diego Knupp, Isabela Florindo Pinheiro
Presenter: Isabela Florindo Pinheiro
doi://10.26678/ABCM.COBEM2017.COB17-1542
Abstract
This paper is focused on the solution of eigenvalue problems for irregular-shaped domains using the Generalized Integral Transform Technique (GITT). Two-dimensional Helmholtz problems in cartesian coordinates with Dirichlet boundary conditions are used as test-cases with a semi-circular region with angles φ = 90º and φ = 180º. The solution of the eigenproblem is carried out by using an auxiliary problem constructed from simpler 1D eigenfunctions as a basis for expanding the sough solution, and two-different approaches are comparative analyzed. The first is based on using an auxiliary problem defined within the same region as the original problem (the coincident domain approach – CDA), while the second relies on using an auxiliary problem defined in a fictitious domain, obtained from expanding the original domain to a larger regular domain (the fictitious domain approach – FDA). The solutions are verified by comparing the calculated results of the semi-circular domain with the exact analytical solution obtained by employing cylindrical coordinates.
Keywords
Irregular domains, GITT, Eigenproblem, Symbolical Computation
