uu.seUppsala University Publications

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Finite Difference and Discontinuous Galerkin Methods for Wave EquationsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2017 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis, 2017. , p. 53
##### Series

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1522
##### Keywords [en]

Wave propagation, Finite difference method, Discontinuous Galerkin method, Stability, Accuracy, Summation by parts, Normal mode analysis
##### National Category

Computational Mathematics
##### Research subject

Scientific Computing with specialization in Numerical Analysis
##### Identifiers

URN: urn:nbn:se:uu:diva-320614ISBN: 978-91-554-9927-3 (print)OAI: oai:DiVA.org:uu-320614DiVA, id: diva2:1090174
##### Public defence

2017-06-13, Room 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
##### Opponent

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##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt446",{id:"formSmash:j_idt446",widgetVar:"widget_formSmash_j_idt446",multiple:true}); Available from: 2017-05-22 Created: 2017-04-23 Last updated: 2017-06-28
##### List of papers

Wave propagation problems can be modeled by partial differential equations. In this thesis, we study wave propagation in fluids and in solids, modeled by the acoustic wave equation and the elastic wave equation, respectively. In real-world applications, waves often propagate in heterogeneous media with complex geometries, which makes it impossible to derive exact solutions to the governing equations. Alternatively, we seek approximated solutions by constructing numerical methods and implementing on modern computers. An efficient numerical method produces accurate approximations at low computational cost.

There are many choices of numerical methods for solving partial differential equations. Which method is more efficient than the others depends on the particular problem we consider. In this thesis, we study two numerical methods: the finite difference method and the discontinuous Galerkin method. The finite difference method is conceptually simple and easy to implement, but has difficulties in handling complex geometries of the computational domain. We construct high order finite difference methods for wave propagation in heterogeneous media with complex geometries. In addition, we derive error estimates to a class of finite difference operators applied to the acoustic wave equation. The discontinuous Galerkin method is flexible with complex geometries. Moreover, the discontinuous nature between elements makes the method suitable for multiphysics problems. We use an energy based discontinuous Galerkin method to solve a coupled acoustic-elastic problem.

1. High order finite difference methods for the wave equation with non-conforming grid interfaces$(function(){PrimeFaces.cw("OverlayPanel","overlay861408",{id:"formSmash:j_idt495:0:j_idt499",widgetVar:"overlay861408",target:"formSmash:j_idt495:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. An improved high order finite difference method for non-conforming grid interfaces for the wave equation$(function(){PrimeFaces.cw("OverlayPanel","overlay1090156",{id:"formSmash:j_idt495:1:j_idt499",widgetVar:"overlay1090156",target:"formSmash:j_idt495:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Convergence of summation-by-parts finite difference methods for the wave equation$(function(){PrimeFaces.cw("OverlayPanel","overlay861401",{id:"formSmash:j_idt495:2:j_idt499",widgetVar:"overlay861401",target:"formSmash:j_idt495:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Convergence of finite difference methods for the wave equation in two space dimensions$(function(){PrimeFaces.cw("OverlayPanel","overlay1090158",{id:"formSmash:j_idt495:3:j_idt499",widgetVar:"overlay1090158",target:"formSmash:j_idt495:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. An energy based discontinuous Galerkin method for acoustic–elastic waves$(function(){PrimeFaces.cw("OverlayPanel","overlay1090157",{id:"formSmash:j_idt495:4:j_idt499",widgetVar:"overlay1090157",target:"formSmash:j_idt495:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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