Absorbing Boundary Conditions For Corner Regions

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dc.contributor.advisor Dr. Hassan, T., Committee Member en_US
dc.contributor.advisor Dr. G. Mahinthakumar, Committee Member en_US
dc.contributor.advisor Dr. Guddati, M. N., Committee Chair en_US
dc.contributor.author Lim, Keng Wit en_US
dc.date.accessioned 2010-04-02T17:55:06Z
dc.date.available 2010-04-02T17:55:06Z
dc.date.issued 2003-10-30 en_US
dc.identifier.other etd-10292003-195531 en_US
dc.identifier.uri http://www.lib.ncsu.edu/resolver/1840.16/391
dc.description.abstract This thesis contains the work that extends the continued fraction absorbing boundary conditions (CFABC's) to corner regions. We combine the ideas related to optimal discretization of perfectly matched layers (PML's) presented by Asvadurov et al. and the continued fraction expansion of one-way wave equations through finite element discretization given by Guddati to arrive at the new formulation of the CFABC and its extension to corner regions. It will be shown that CFABC is a special case of the discrete PML, where CFABC is obtained from PML as a result of finite element discretization of the PML via one-point integration with purely imaginary element length. Discretization of the two-dimensional corner region is performed as a tensor product of the two CFABC one-dimensional discretization, which when viewed from the PML approach, is equivalent to discretizing the Helmholtz equation where pure imaginary stretching function and 1 by 1 integration are used. Extension to non-orthogonal corners by the use of parallelogram elements is also performed. The result is that the dynamic stiffness matrix is independent of frequency, resulting in identical matrix entries in both the wave number-frequency and space-time domain. The dynamic stiffness matrix simply becomes the element stiffness matrix in the space-time domain. This allows for extremely easy finite element implementation for both transient and time-harmonic cases. An implicit scheme is currently being used with the CFABC. A full explicit scheme is not possible since the mass matrix is singular (the absorbing boundary conditions do not contribute to the mass matrix. The second part of the thesis deals with the exploration of a pseudo-explicit time stepping scheme for the CFABC's. Currently, the implementation is limited to the case of straight computational boundaries. This initial work, together with the computer code developed, will provide a reference for the future improvement of the scheme. en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject absorbing boundary conditions en_US
dc.subject perfectly matched layers en_US
dc.subject continued fraction absorbing boundary conditions en_US
dc.subject wave propagation en_US
dc.title Absorbing Boundary Conditions For Corner Regions en_US
dc.degree.name MS en_US
dc.degree.level thesis en_US
dc.degree.discipline Civil Engineering en_US


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