Page 12 - Winter 2020

COMPUTATIONAL ACOUSTICS METHODS
Table 1. Some relevant articles published in Acoustics Today
same techniques used in those areas can be applied in other areas (see Table 1 for articles in Acoustics Today that discuss the use of similar techniques).
In addition, applications of machine learning (ML) that are being used in artificial intelligence research and areas of data science are also being exploited to advance research into areas including acoustic oceanography, engineering acoustics, and signal processing. This is by no means an exhaustive list, but it brings a familiarization to the areas and applications of computational acoustics and the methods found therein.
Modern Computational Methods
The numerical methods of computational acoustics are focused on taking the continuous equations and differ- ential equations from calculus and turning them into linear algebraic equations, which are amenable to solu- tion on digital computers. In the case of a concert hall with complex geometries that are not open to an ana- lytic solution, computational acoustics would enable an acoustics engineer to compute a numerical solution to the wave equation to help the engineering design process, as discussed recently by Savioja and Xiang (2020).
Two of the more popular methods are the finite-differ- ence method (FDM) and finite-element method (FEM). The FDM is a class of numerical techniques related to a general class of numerical methods known as Galerkin methods (Jensen et al., 2011; Wang et. al., 2019) that treat
derivatives as algebraic differences and the continuous function in question, such as the sound field, is calculated at various points of space (Botteldooren, 1994).
For example, Figure 2 shows how to break up the space with a grid where the sound field is calculated t as an individual element in space. Each point is calculated through iteration via a computational algorithm. The calculations are often simple enough that they could be performed with pencil and paper or a basic calculator. However, if the procedure needs to be applied to many points, there may need to be thousands to millions of computations, thereby requiring a digital computer.
In contrast to the FDM, the FEM is another numerical tech- nique used for calculating sound fields based on dividing up aspaceorstructureintoindividualelements,eachofwhich is assumed to be constant. The space/structure is broken
Authors
Topic
Ahrens et. al., 2014
Sound field synthesis
Bruce, 2017
Speech intelligibility, signal processing
Bunting et. al., 2020
Computational acoustics
Burnett, 2015
Computer simulation of scattering
Candy, 2008
Signal processing, model-based machine learning beginnings
Duda, et. al., 2019
Ocean acoustics
Greenberg, 2018
Deep learning, languages
Hambri and Fahnline, 2007
Structural acoustics, modeling methods
Hawley et. al., 2020
Musical acoustics
Puria, 2020
Bioacoustics, hearing
Stone and Shadle, 2016
Speech production, modeling, computational fluid dynamics
Treeby, 2019
Biomedical acoustics
Vorländer, 2020
Virtual reality and music
Wage, 2018
Array signal processing and localization
Wilson et. al., 2015
Atmospheric acoustic propagation
Zurk, 2018
Underwater acoustic sensing
These papers have either a computational focus or computational relationship.
ways to investigate interactions that previously were unap- proachable due to the complex nature of acoustics.
Computational acoustics, which is a combination of math- ematical modeling and numerical solution algorithms, has recently emerged as a subdiscipline of acoustics. The use of approximation techniques to calculate acoustic fields with computer-based models and simulations allows for previously unapproachable problems to be solved.
The increasing computational nature of acoustics, especially in all the traditional areas, has provided a cross-disciplinary opportunity. The purpose of this paper is to show an overview of the various techniques used in computational acoustics over several of the traditional areas. I am more familiar with applications in under- water acoustics and physical acoustics, but many of the
12 Acoustics Today • Spring 2021