Hybrid convolution quadrature methods for modelling time-dependent waves with broadband frequency content

Rowbottom, J., 2021. Hybrid convolution quadrature methods for modelling time-dependent waves with broadband frequency content. PhD, Nottingham Trent University.

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Abstract

This work proposes two new hybrid convolution quadrature based discretisations of the wave equation for interior domains with broadband Neumann boundary data or source terms. The convolution quadrature method transforms the time domain wave problem into a series of Helmholtz problems with complex-valued wavenumbers, in which the boundary data and solutions are connected to those of the original problem through the Z-transform. The hybrid method terminology refers specifically to the use of different approximations of these Helmholtz problems, depending on the frequency. For lower frequencies we employ the boundary element method, while for more oscillatory problems we develop two alternative high frequency approximations based on plane wave decompositions of the acoustic field on the boundary. In the first approach we apply dynamical energy analysis to numerically approximate the plane wave amplitudes. The phases will then be reconstructed using a novel approach based on matching the boundary element solution to the plane wave ansatz in the frequency region where we switch between the low and high frequency methods. The second high frequency method is based on applying the Neumann-to Dirichlet map for plane waves to the given boundary data.

Item Type: Thesis
Creators: Rowbottom, J.
Date: September 2021
Rights: The copyright in this work is held by the author. You may copy up to 5% of this work for private study, or personal, non-commercial research. Any re-use of the information contained within this document should be fully referenced, quoting the author, title, university, degree level and pagination. Queries or requests for any other use, or if a more substantial copy is required, should be directed to the author.
Divisions: Schools > School of Science and Technology
Record created by: Linda Sullivan
Date Added: 28 Jun 2022 14:16
Last Modified: 28 Jun 2022 14:16
URI: http://irep.ntu.ac.uk/id/eprint/46498

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