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A high-order accurate, collocated boundary element method for wave propagation in layered media
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The ultimate goal of this research is to construct a hybrid model for sound propagation in layered underwater environments with curved boundaries by employing a differential formulation for inhomogeneous layers and a boundary integral formulation for homogeneous layers. The discretization of the new hybrid model is a combination of a finite difference method for the Helmholtz equation for inhomogeneous media and a collocated boundary element method (BEM) for the integral equation for homogeneous media, while taking special care of the open boundaries and the common interface.

Our focus is on sound wave propagation in layered piecewise homogeneous fluid media. A boundary integral formulation of the Helmholtz equation governing the acoustic pressure is employed. A fourth-order accurate, collocated BEM is constructed for this equation in a systematic way, facilitating its generalization to even higher orders of accuracy.

A novel approach (for boundary element techniques) is proposed for modelling the open vertical boundaries. We introduce artificial near- and far-field boundaries and apply nonlocal radiation boundary conditions at these.

The collocated BEM is implemented in Matlab and the numerical experiments show the expected convergence rate.

A strong benefit of the collocated BEM is that only the boundary is discretized, thus, reducing the number of dimensions by one. By a comparison with a fourth-order finite difference method (FD) it is illustrated that both methods have memory requirements of the same order, however, the number of unknowns in the collocated BEM is an order of magnitude less than in FD and the ratio grows with the problem size.

Place, publisher, year, edition, pages
Uppsala University, 2011.
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2011-005
National Category
Computational Mathematics
Research subject
Numerical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-157834OAI: oai:DiVA.org:uu-157834DiVA: diva2:436445
Supervisors
Available from: 2011-09-16 Created: 2011-08-23 Last updated: 2017-08-31Bibliographically approved
List of papers
1. Discretization of a hybrid model for acoustic wave propagation in layered fluid media
Open this publication in new window or tab >>Discretization of a hybrid model for acoustic wave propagation in layered fluid media
2011 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-015
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-155491 (URN)
Available from: 2011-06-22 Created: 2011-06-22 Last updated: 2011-11-18Bibliographically approved
2. Implementation of a collocated boundary element method for acoustic wave propagation in multilayered fluid media
Open this publication in new window or tab >>Implementation of a collocated boundary element method for acoustic wave propagation in multilayered fluid media
2011 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-016
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-155492 (URN)
Available from: 2011-06-23 Created: 2011-06-23 Last updated: 2011-11-18Bibliographically approved

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CiteExportLink to record
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Citation style
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