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An energy based discontinuous Galerkin method for acoustic–elastic waves
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
2017 (engelsk)Inngår i: Proc. 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Minneapolis, MN: University of Minnesota Press, 2017, s. 389-390Konferansepaper, Oral presentation with published abstract (Annet vitenskapelig)
sted, utgiver, år, opplag, sider
Minneapolis, MN: University of Minnesota Press, 2017. s. 389-390
HSV kategori
Identifikatorer
URN: urn:nbn:se:uu:diva-320601OAI: oai:DiVA.org:uu-320601DiVA, id: diva2:1090157
Konferanse
WAVES 2017
Tilgjengelig fra: 2017-05-19 Laget: 2017-04-23 Sist oppdatert: 2017-06-30bibliografisk kontrollert
Inngår i avhandling
1. Finite Difference and Discontinuous Galerkin Methods for Wave Equations
Åpne denne publikasjonen i ny fane eller vindu >>Finite Difference and Discontinuous Galerkin Methods for Wave Equations
2017 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

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.

sted, utgiver, år, opplag, sider
Uppsala: Acta Universitatis Upsaliensis, 2017. s. 53
Serie
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1522
Emneord
Wave propagation, Finite difference method, Discontinuous Galerkin method, Stability, Accuracy, Summation by parts, Normal mode analysis
HSV kategori
Forskningsprogram
Beräkningsvetenskap med inriktning mot numerisk analys
Identifikatorer
urn:nbn:se:uu:diva-320614 (URN)978-91-554-9927-3 (ISBN)
Disputas
2017-06-13, Room 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 10:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2017-05-22 Laget: 2017-04-23 Sist oppdatert: 2017-06-28

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