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Accurate and Well-posed Absorbing Boundary Conditions for Anisotropic Media.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Accurate and Well-posed Absorbing Boundary Conditions for Anisotropic Media./
Author:	Savadatti, Siddharth.
Description:	231 p.
Notes:	Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: .
Contained By:	Dissertation Abstracts International73-06B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3497304
ISBN:	9781267179753

Accurate and Well-posed Absorbing Boundary Conditions for Anisotropic Media.
Savadatti, Siddharth.

Accurate and Well-posed Absorbing Boundary Conditions for Anisotropic Media. - 231 p.

Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: .

Thesis (Ph.D.)--North Carolina State University, 2011.

This dissertation provides (a) an accurate and well-posed local absorbing boundary condition (ABC) for time-dependent modeling of propagating waves in tilted anisotropic acoustic media, (b) an accurate local ABC for time-harmonic modeling of both propagating and evanescent anti-plane and in-plane waves in tilted elliptic anisotropic elastic media, and (c) an accurate local ABC for time-harmonic modeling of in-plane propagating waves in untilted non-elliptic anisotropic elastic media. Such media support wavemodes with opposing signs of phase (cpx) and group (cgx) velocities that have long posed a significant challenge to the design of accurate, well-posed and stable local ABCs. By specifically considering the recently developed local ABC, the perfectly matched discrete layer (PMDL), we show that a careful choice of parameters can result in an effective local ABC for anisotropic media.

ISBN: 9781267179753Subjects--Topical Terms:

845450
Applied Mechanics.

Accurate and Well-posed Absorbing Boundary Conditions for Anisotropic Media.
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035 $a (UMI)AAI3497304
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100 1 $a Savadatti, Siddharth. $3 845543
245 1 0 $a Accurate and Well-posed Absorbing Boundary Conditions for Anisotropic Media.
300 $a 231 p.
500 $a Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: .
500 $a Adviser: Murthy N. Guddati.
502 $a Thesis (Ph.D.)--North Carolina State University, 2011.
520 $a This dissertation provides (a) an accurate and well-posed local absorbing boundary condition (ABC) for time-dependent modeling of propagating waves in tilted anisotropic acoustic media, (b) an accurate local ABC for time-harmonic modeling of both propagating and evanescent anti-plane and in-plane waves in tilted elliptic anisotropic elastic media, and (c) an accurate local ABC for time-harmonic modeling of in-plane propagating waves in untilted non-elliptic anisotropic elastic media. Such media support wavemodes with opposing signs of phase (cpx) and group (cgx) velocities that have long posed a significant challenge to the design of accurate, well-posed and stable local ABCs. By specifically considering the recently developed local ABC, the perfectly matched discrete layer (PMDL), we show that a careful choice of parameters can result in an effective local ABC for anisotropic media.
520 $a We first consider a PMDL with real-valued parameters designed to absorb the propagating wavemodes of tilted anisotropic acoustics. Starting with the derivation of the reflection coefficient, we show that the PMDL absorption is based on group (not phase) velocities. The group velocity form of the reflection coefficient is used to derive a sufficient condition for PMDL to accurately absorb all outgoing wavemodes (even those with opposing signs of phase and group velocities, i.e. cpxcgx < 0) and this condition turns out to be a simple bound on the PMDL parameters. By deriving the necessary and sufficient condition for the well-posedness of the initial boundary value problem (IBVP) obtained by coupling an interior with PMDL, we show that the accuracy condition also ensures well-posedness.
520 $a We consider next a PMDL with complex-valued parameters designed to absorb both the propagating and evanescent wavemodes of tilted elliptic anisotropic elasticity. By first considering the simpler case of scalar anti-plane shear waves, we show that it is possible to overcome the challenges posed by cpxcgx < 0, in fact by taking advantage of what are considered unwanted and inevitable reflections occurring at the truncation boundaries. This understanding helps us explain the ability of PMDL to accurately model media with cpxcgx < 0 without the need of intervening space-time transformations; while space-time transformations have been traditionally used to treat wavemodes with cpxcgx < 0, their extension to heterogeneous (layered) media is unclear. The approximation properties of PMDL quantified through its reflection matrix is used to derive simple bounds on the PMDL parameters necessary for the accurate absorption of all outgoing anti-plane and in-plane wavemodes.
520 $a We finally consider a PMDL with real-valued parameters designed to absorb the propagating wavemodes of untilted non-elliptic anisotropic elasticity. While simple space-time transformations are available to treat the wavemodes with cpxcgx < 0 present in elliptic anisotropic media, no such transformations are known to exist for the non-elliptic case; by using the concept of layer grouping along with a stretching of the finite element mesh, we present an unconventional spatial transformation that guarantees accuracy. The approximation properties of PMDL revealed through its reflection matrix allow us to (a) show that it is impossible to design an accurate PMDL with wavenumber-independent parameters, (b) demonstrate theoretically, the ability of wavenumber-dependent parameters to ensure accuracy, and finally (c) design a practical though unconventional stretching of the finite element PMDL mesh that facilitates the implementation of wavenumber-dependent parameters.
520 $a Existing knowledge points to the fact that effective local ABCs can be designed for elliptic anisotropic media only through appropriate space-time transformations and no such transformations are available for non-elliptic anisotropic media. This dissertation proves that: (a) it is possible to design an effective local ABC for elliptic anisotropic media without the use of space-time transformations, and (b) there exists a space-time transformation for nonelliptic anisotropic media---at least in the untilted case.
590 $a School code: 0155.
650 4 $a Applied Mechanics. $3 845450
650 4 $a Applied Mathematics. $3 845392
650 4 $a Geophysics. $3 686174
690 $a 0346
690 $a 0364
690 $a 0373
710 2 $a North Carolina State University. $3 845424
773 0 $t Dissertation Abstracts International $g 73-06B.
790 1 0 $a Guddati, Murthy N., $e advisor
790 $a 0155
791 $a Ph.D.
792 $a 2011
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3497304