Name: THIAGO GALDINO BALISTA

Publication date: 17/12/2021
Advisor:

Name	Role
LUCIANO DE OLIVEIRA CASTRO LARA	Advisor *

Examining board:

Name	Role
CARLOS FRIEDRICH LOEFFLER NETO	Co advisor *
HERCULES DE MELO BARCELOS	External Examiner *
LUCIANO DE OLIVEIRA CASTRO LARA	Advisor *
WELLINGTON BETENCURTE DA SILVA	Internal Examiner *

Summary: This work deals with the application of the Boundary Element Method (BEM) to solve problems governed by the Helmholtz Equation. For this, we use the adaptive procedure called Direct Interpolation Self-regularized (DIBEM-2), which applies radial basis functions to solve the integral term referring to the inertia in the Helmholtz Equation. This new technique originated from the formulation Direct Interpolation (DIBEM). However, the DIBEM-2 technique establishes an auxiliary function, which consists of the fundamental solution of the Laplace problem subtracted from a function associated with the Galerkin Tensor and, in this way, ignores the execution of the regularization procedure, since it avoids the singularity produced in the fundamental solution due to the coincidence between the source points and the interpolation points. In a second step, the BEM formulation is proposed by extending the application of Multiple Reciprocity (MRBEM) which strategically uses a sequence of fundamental higher-order solutions, collaborating to convert the domain integral term to the exact contour only using the proposed formulation. Thus, numerical experiments are implemented on two-dimensional problems in order to evaluate the performance of the two proposals by solving the response problem, which corresponds to sweeping different excitation frequencies. In general, simulations are compared with analytical solutions to generate benchmark information

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