Boundary waves and stability of the perfectly matched layer II: extensions to first order systems and numerical stability

dc.contributor.authorDuru, Kenneth
dc.contributor.authorKozdon, Jeremy E.
dc.contributor.authorKreiss, Gunilla
dc.contributor.departmentApplied Mathematics
dc.date.accessioned2014-05-29T22:23:53Z
dc.date.available2014-05-29T22:23:53Z
dc.date.issued2012
dc.description.abstractIn this paper we study the stability of the perfectly matched layer (PML) for the elastic wave equation in rst order form. The theory of temporal stability of initial value problems corresponding to the PML is well developed. For initial boundary value problems (IBVPs) the theory of temporal stability of the PML is less complete. First, we study the solutions of two IBVPs corresponding to the PML for the elastic wave equation in rst order form. We consider separately a PML on the lower half-plane with free-surface boundary conditions at y = 0 and a PML on the left half-plane with characteristic boundary conditions at x = . In both cases the PML truncates a boundary in the x{direction. Using normal mode analysis we prove that the lower half{plane problem and the left half{plane problem do not support temporally growing modes. Second, we develop a high order accurate nite di erence approximation of the PML subject to the boundary conditions. To enable accurate and stable boundary treatments for the PML we construct continuous energy estimates in the Laplace space. We use summation-by-parts nite di erence operators to approximate the spatial derivatives and impose boundary conditions weakly using penalties. By mimicking the continuous energy estimates in the discrete setting, we construct stable numerical boundary procedures for the PML subject to the free-surface and the characteristic boundary conditions. Numerical experiments are presented corroborating the theoretical results.en_US
dc.identifier.urihttps://hdl.handle.net/10945/41701
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.subject.authorelastic wave equationen_US
dc.subject.authorrst order systemsen_US
dc.subject.authorRayleigh surface wavesen_US
dc.subject.authorperfectly matched layersen_US
dc.subject.authorstabilityen_US
dc.subject.authornormal mode analysisen_US
dc.subject.authorhigh order nite di erenceen_US
dc.subject.authorsummation{by{partsen_US
dc.subject.authorpenalty methoden_US
dc.titleBoundary waves and stability of the perfectly matched layer II: extensions to first order systems and numerical stabilityen_US
dc.typeArticleen_US
dspace.entity.typePublication
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