Fully automatic hp-adaptivity for acoustic and electromagnetic scattering in three dimensions

dc.contributor.advisorDemkowicz, Leszeken
dc.creatorKurtz, Jason Patrick, 1979-en
dc.date.accessioned2008-08-28T23:29:54Zen
dc.date.accessioned2017-05-11T22:17:45Z
dc.date.available2008-08-28T23:29:54Zen
dc.date.available2017-05-11T22:17:45Z
dc.date.issued2007-05en
dc.descriptiontexten
dc.description.abstractWe present an algorithm for fully automatic hp-adaptivity for finite element approximations of elliptic and Maxwell boundary value problems in three dimensions. The algorithm automatically generates a sequence of coarse grids, and a corresponding sequence of fine grids, such that the energy norm of error decreases exponentially with respect to the number of degrees of freedom in either sequence. At each step, we employ a discrete optimization algorithm to determine the refinements for the current coarse grid such that the projection-based interpolation error for the current fine grid solution decreases with an optimal rate with respect to the number of degrees of freedom added by the refinement. The refinements are restricted only by the requirement that the resulting mesh is at most 1-irregular, but they may be anisotropic in both element size h and order of approximation p. While we cannot prove that our method converges at all, we present numerical evidence of exponential convergence for a diverse suite of model problems from acoustic and electromagnetic scattering. In particular we show that our method is well suited to the automatic resolution of exterior problems truncated by the introduction of a perfectly matched layer. To enable and accelerate the solution of these problems on commodity hardware, we include a detailed account of three critical aspects of our implementations, namely an efficient implementations of sum factorization, several interfaces to the direct multi-frontal solver MUMPS, and some fast direct solvers for the computation of a sequence of nested projections.en
dc.description.departmentComputational Science, Engineering, and Mathematicsen
dc.description.departmentComputational and Applied Mathematicsen
dc.format.mediumelectronicen
dc.identifierb6878305xen
dc.identifier.oclc173515277en
dc.identifier.urihttp://hdl.handle.net/2152/3142en
dc.language.isoengen
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshFinite element methoden
dc.subject.lcshScattering (Physics)en
dc.subject.lcshBoundary value problems--Numerical solutionsen
dc.titleFully automatic hp-adaptivity for acoustic and electromagnetic scattering in three dimensionsen
dc.type.genreThesisen

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