An improvement to the frequency response in non-homogeneous Helmholtz problem using the Double Fictitious Background Media Formulation

Resumo

This article proposes a new formulation of the Boundary Elements Method to solve the response
problem in non-homogeneous Helmholtz problems, called Double Fictitious Background Media (DFBMF). The
DFBMF is based on a simple algebraic procedure, creating a fictitious medium, which consists of adding and
subtracting the same term in the governing equation, which divides it into two parts: a homogeneous Helmholtz
equation and a fictitious reactive term. This new governing differential equation is mathematically independent of
the properties of the chosen fictional background medium. Still, considering the Weighted Residual Principles, the
associated integral boundary equation is affected by the Green Function argument through the reactive term, which
accounts for the variation in physical properties. To reduce the numerical error, two integral equations with
different arguments are generated where the reactive term is considered a common source to the two equations.
The numerical simulations show a significant increase in the precision of the results with the application of this
strategy.