Compact High-order Finite Difference Schemes for Acoustic Wave Equations

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dc.contributor.advisorLiao, Wenyuan
dc.contributor.authorLi, Keran
dc.contributor.committeememberLamoureux, Michael P.
dc.contributor.committeememberLiao, Wenyuan
dc.contributor.committeememberBraverman, Elena
dc.contributor.committeememberLiang, Dong
dc.contributor.committeememberWare, Antony Frank
dc.date2021-06
dc.date.accessioned2021-01-06T23:19:38Z
dc.date.available2021-01-06T23:19:38Z
dc.date.issued2021-01-05
dc.description.abstractThis study developed three compact high-order finite difference schemes for acoustic wave equations. Benefiting from the compactness, the new schemes require less layers of boundary conditions than conventional finite difference schemes. All the three schemes work for acoustic wave equations with variable coefficients in homogeneous media, with the third one also being applicable to the case of heterogeneous density media. The first scheme is based on Padé approximation which is formally a product of the inverse of a finite difference operator and the conventional 2nd-order finite difference operator, thus some algebraic manipulation is necessary to discuss the product of operators. The second scheme is based on so-called combined finite difference method, which needs the boundary conditions for the second spatial derivatives and the needed boundary conditions can be derived by using the wave equation and usual Dirichlet boundary conditions themselves. The third scheme is also based on combined finite difference method, and it generalizes the second scheme so that it can also work in heterogeneous density media case, i.e., the Laplacian in the wave equations being divergence form. The stability of the first two schemes are established by an energy method, while the stability of the last scheme is obtained by an analogy of von Neumann analysis. All of these new schemes are proven to be conditionally stable with given Courant-Friedrichs-Lewy (CFL) numbers. Numerical experiments are conducted to verify the efficiency, accuracy and stability of the new schemes. It is expected that these new schemes will find extensive applications in both research and engineering areas.en_US
dc.identifier.citationLi, K. (2021). Compact High-order Finite Difference Schemes for Acoustic Wave Equations (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/38531
dc.identifier.urihttp://hdl.handle.net/1880/112939
dc.language.isoengen_US
dc.publisher.facultyScienceen_US
dc.publisher.institutionUniversity of Calgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.en_US
dc.subjectCompact Finite Difference Schemeen_US
dc.subjectAcoustic Wave Equationen_US
dc.subjectHigh-order Schemeen_US
dc.subject.classificationEducation--Mathematicsen_US
dc.titleCompact High-order Finite Difference Schemes for Acoustic Wave Equationsen_US
dc.typedoctoral thesisen_US
thesis.degree.disciplineMathematics & Statisticsen_US
thesis.degree.grantorUniversity of Calgaryen_US
thesis.degree.nameDoctor of Philosophy (PhD)en_US
ucalgary.item.requestcopytrueen_US
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