O Método dos Elementos de Contorno com Interpolação Direta e Técnica de Superposição de Domínio aplicado a problemas de Helmholtz em meios suavemente heterogêneos

Resumo

This paper presents the coupling between the Direct Interpolation Boundary Element Method
(DIBEM) and the Domain Superposition Technique (DST) addressing problems governed by the
inhomogeneous Helmholtz’s Equation. Specifically, here are approached cases in which the constitutive medium
property varies smoothly according to a known function. As the constitutive properties can be located in
piecewise sectors, the Domain Superposition Technique (DST) is used as a way to compute the different
properties, preserving the particularities of the Boundary Elements Method (BEM). Inhomogeneous problems
are usually solved by domain numerical techniques, but using the DIBEM formulation the domain integral
generated by the non-homogeneity of the medium can be accurately transformed into a boundary integral.
Numerical tests are implemented in two-dimensional problems, with regular and irregular domains, imposing, in
the latter case, numerical difficulties on the proposed method. Simulations using the Finite Element Method are
used to generate the reference solutions.