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Uncertainty Quantification Problems in Tsunami Modeling and Reduced Order Models for Hyperbolic Partial Differential Equations.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Uncertainty Quantification Problems in Tsunami Modeling and Reduced Order Models for Hyperbolic Partial Differential Equations./
Author:	Rim, Donsub.
Description:	1 online resource (153 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.
Contained By:	Dissertation Abstracts International79-01B(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355124095

Uncertainty Quantification Problems in Tsunami Modeling and Reduced Order Models for Hyperbolic Partial Differential Equations.
Rim, Donsub.

Uncertainty Quantification Problems in Tsunami Modeling and Reduced Order Models for Hyperbolic Partial Differential Equations. - 1 online resource (153 pages)

Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

In this thesis, we consider an uncertainty quantification (UQ) problem that arises from tsunami modeling, namely the probabilistic tsunami hazard assessment (PTHA) problem. The goal of PTHA is to compute the probability of inundation at coastal communities, and the uncertainty originates from the unknown slip distribution of potential tsunamigenic earthquakes. First, we show that the Karhunen-Loeve (K-L) expansion can be used to generate a wide range of random earthquake scenarios that represent this uncertainty well. Then we propose a multi-resolution approach to estimate the inundation: since it is computationally expensive to accurately estimate the inundation resulting from each scenario by using only fine-grid runs, many cheap coarse-grid runs are used instead to bulid an approximation.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355124095Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Uncertainty Quantification Problems in Tsunami Modeling and Reduced Order Models for Hyperbolic Partial Differential Equations.
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100 1 $a Rim, Donsub. $3 1182474
245 1 0 $a Uncertainty Quantification Problems in Tsunami Modeling and Reduced Order Models for Hyperbolic Partial Differential Equations.
264 0 $c 2017
300 $a 1 online resource (153 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.
500 $a Advisers: Randall J. LeVeque; Gunther A. Uhlmann.
502 $a Thesis (Ph.D.) $c University of Washington $d 2017.
504 $a Includes bibliographical references
520 $a In this thesis, we consider an uncertainty quantification (UQ) problem that arises from tsunami modeling, namely the probabilistic tsunami hazard assessment (PTHA) problem. The goal of PTHA is to compute the probability of inundation at coastal communities, and the uncertainty originates from the unknown slip distribution of potential tsunamigenic earthquakes. First, we show that the Karhunen-Loeve (K-L) expansion can be used to generate a wide range of random earthquake scenarios that represent this uncertainty well. Then we propose a multi-resolution approach to estimate the inundation: since it is computationally expensive to accurately estimate the inundation resulting from each scenario by using only fine-grid runs, many cheap coarse-grid runs are used instead to bulid an approximation.
520 $a For physical models that involve hyperbolic partial differential equations (PDEs), dimensionality reduction techniques such as the K-L expansion or multi-resolution approaches face limitations due to the fact that snapshot matrices built from solutions often exhibit slow decay in singular values, whereas fast decay is crucial for the success of many projection-based model reduction methods. To overcome this problem, we build on previous work in symmetry reduction [Rowley and Marsden, Physica D (2000), pp. 1--19] and propose an iterativealgorithm we call transport reversal that decomposes the snapshot matrix into multiple shifting profiles, each with a corresponding speed in 1D. Its applicability to typical hyperbolic problems is demonstrated through numerical examples, and other natural extensions that modify the shift operator are considered.
520 $a Transport or wave phenomena are much more complicated in multiple spatial dimensions, and in our approach to extend the transport reversal algorithm to higher dimensions it becomes crucial to generalize the large time-step (LTS) operators [LeVeque, SIAM J. Numer. Anal. (1985), pp.1051--1073]. For this purpose, we introduce a dimensional splitting method using the Radon transform, that enables the transport reversal introduced above for 1D to be extended to higher spatial dimensions. This dimensional splitting is of interest in its own right, and its applications to the solution of acoustic equation, absorbing boundary condition and displacement interpolation are illustrated. This splitting method requires inverting the Radon transform, and a method for inversion using conjugate gradient algorithm will be discussed.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Washington. $b Applied Mathematics. $3 1180484
773 0 $t Dissertation Abstracts International $g 79-01B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10598803 $z click for full text (PQDT)