Optimal Finite Difference Schemes for the Helmholtz Equation with PML

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dc.contributor.advisorLiao, Wenyuan
dc.contributor.authorDastour, Hatef
dc.contributor.committeememberWare, Antony Frank
dc.contributor.committeememberLamoureux, Michael P.
dc.contributor.committeememberZinchenko, Yuriy
dc.date2020-06
dc.date.accessioned2019-12-19T22:00:18Z
dc.date.available2019-12-19T22:00:18Z
dc.date.issued2019-12-17
dc.description.abstractAn efficient and accurate numerical scheme for solving the seismic wave equations is a key part in seismic wave propagation modeling. The pollution effect of high wavenumbers (the accuracy of the numerical results often deteriorates as the wavenumber increases) plays a critical role in the accuracy of these numerical schemes and it is inevitable in two and three dimensional Helmholtz equations. Optimal finite difference methods can offer a remedy to this problem; however, the numerical solution to a multi-dimensional Helmholtz equation can be troublesome when the perfectly matched layer (PML) boundary condition is implemented. This study develops a number of optimal finite difference schemes for solving the Helmholtz equation in the presence of PML. In doing so, we implement two common strategies, derivative-weighting and point-weighting strategies, for constructing these schemes. Furthermore, a challenge for developing such methods is being consistent with the Helmholtz equation with PML. Thus, analytical and numerical proofs are provided to show the consistency of the schemes. Moreover, for each developed optimal finite difference method, error analysis for the numerical approximation of the exact wavenumber is provided. Based on minimizing the numerical dispersion, some optimal parameters strategies for each optimal finite difference schemes are recommended. Furthermore, several examples are provided to illustrate the accuracy and effectiveness of the new methods in reducing numerical dispersion.en_US
dc.identifier.citationDastour, H. (2019). Optimal Finite Difference Schemes for the Helmholtz Equation with PML (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/37353
dc.identifier.urihttp://hdl.handle.net/1880/111362
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.subjectHelmholtz Equationen_US
dc.subjectPerfectly Matched Layeren_US
dc.subjectOptimal Finite Difference Schemeen_US
dc.subjectNumerical Dispersionen_US
dc.subject.classificationMathematicsen_US
dc.titleOptimal Finite Difference Schemes for the Helmholtz Equation with PMLen_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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