Subscribe: IMA Journal of Applied Mathematics - Advance Access
Preview: IMA Journal of Applied Mathematics - Advance Access

IMA Journal of Applied Mathematics Advance Access

Published: Tue, 05 Sep 2017 00:00:00 GMT

Last Build Date: Tue, 05 Sep 2017 03:48:07 GMT


A pipe organ-inspired ultrasonic transducer


This article considers a number of backplate designs for the bandwidth improvement of electrostatic ultrasonic transducers in both transmission and reception modes. Motivated by the design of pipe organs, transducers with backplates which incorporate a number of acoustically resonating conduits are modelled using a transmission line mathematical model which describes the displacement of the electrostatic membrane. The model illustrates that by increasing the number and varying the length of these conduits, the transmission voltage response and the reception force response can be improved over the traditional design by around 50 and 35%, respectively.

Schur complement domain decomposition methods for the solution of multiple scattering problems


We present a Schur complement domain decomposition (DD) algorithm for the solution of frequency domain multiple scattering problems. Just as in the classical DD methods, we (1) enclose the ensemble of scatterers in a domain bounded by an artificial boundary, (2) we subdivide this domain into a collection of non-overlapping subdomains so that the boundaries of the subdomains do not intersect any of the scatterers and (3) we connect the solutions of the subproblems via Robin boundary conditions matching on the common interfaces between subdomains. We use subdomain Robin-to-Robin maps to recast the DD problem as a sparse linear system whose unknown consists of Robin data on the interfaces between subdomains—two unknowns per interface. The Robin-to-Robin maps are computed in terms of well conditioned boundary integral operators, and thus the method of solution proposed in this paper can be viewed as a boundary integral equation (BIE)/BIE coupling via artificial subdomains. Unlike classical DD, we do not reformulate the DD problem in the form a fixed point iteration, but rather we solve the ensuing linear system by Gaussian elimination of the unknowns corresponding to inner interfaces between subdomains via Schur complements. Once all the unknowns corresponding to inner subdomains interfaces have been eliminated, we solve a much smaller linear system involving unknowns on the inner and outer artificial boundary. We present numerical evidence that our Schur complement DD algorithm can produce accurate solutions of very large multiple scattering problems that are out of reach for other existing approaches.