The Special Interest Group for Mathematical Analysis in Acoustics (SIG-MAA) brings together researchers developing and applying tools from the mathematical fields of applied, numerical and asymptotic analysis in the context of acoustics. Key challenge areas to be addressed include the analysis of propagation in complex domains (e.g. with multiscale structure and/or complicated geometries), the development of effective methods for high frequency problems (in particular, the study of canonical problems arising in the Geometrical Theory of Diffraction), and the rigorous analysis and validation of computational methods.
Mathematical tools that can be applied to such problems include Wiener-Hopf methods, high- and low-frequency asymptotic methods, homogenization, Green’s functions, the unified transform method, boundary integral equations and the theory of special functions. A particular goal of the SIG will be to explore various possibilities for the hybridisation of these diverse techniques in order to develop new tools for the mathematical study of acoustics problems. Since mathematical analysis underpins many of the quantitative tools used in acoustics applications, the SIG-MAA will interact closely with other SIGs to share ideas and promote cross-disciplinary collaboration. In particular we expect strong interaction with members of the Computational Acoustics, Physical Acoustics, Aeroacoustics and Metamaterials SIGs.
In the first instance there will be a conference organised to bring together both established and early-career researchers from across applied, numerical and asymptotic analysis in acoustics. This will provide an opportunity to exchange ideas and promote discussion between researchers of various disciplines, and to provide a comprehensive picture of the corresponding recent research in the UK. Upon consultation with the group members the SIG-MAA will organise future events in order to best support the research and collaboration efforts of the community. These events can include summer schools for in-depth knowledge transfer, as well as workshops and short meetings for discussion of challenges at the forefront of current research.