Isogeometric Analysis and Non-Polynomial Enrichment for Finite Element Methods in Acoustics

Frequency response is necessary to evaluate acoustic parameters such as reverberation times and the clarity of speech or music, or to auralize or visualise an acoustic field. The finite element method (FEM) can accurately capture acoustic wave propagation, interference and diffraction as well as be used for modelling sound diffusers and absorbers in the frequency domain by approximately solving the Helmholtz equation. However, FEM experiences serious limitations in solving acoustical problems at high frequencies when a fixed level of discretization per wavelength is used. In such cases the numerical error from FEM grows rapidly as frequency increases. This issue can be tackled by using high-order approximations in the method and, hence, significantly increase the range of frequencies that can be dealt with. In the last two decades the FEM for modelling acoustic fields has seen major advancements related to incorporating exponential functions in the finite element approximation and the use of non-uniform rational basis spline. The book focuses on developments in these two directions where such elements are introduced and discussed in detail for different types of applications.

This shortform book is essential for engineers seeking industrial applications and remains accessible for graduate students interested in this area of study.