Fast Method for High-Frequency Acoustic Scattering From Random Scatterers

Tsuji, Paul H.; Xiu, Dongbin; Ying, Lexing

doi:10.1615/int.j.uncertaintyquantification.v1.i2.10

Cited by 4 publications

(1 citation statement)

References 26 publications

(37 reference statements)

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“…The motivation for establishing well-posedness and proving a priori bounds on the solution of (1.1) is the growing interest in Uncertainty Quantification (UQ) for the Helmholtz equation; see e.g. [62,58,9,27,23,24,43,36,4]. (In this PDE context, by 'UQ' we mean theory and algorithms for computing statistics of quantities of interest involving PDEs either posed on a random domain or having random coefficients.)…”

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confidence: 99%

The Helmholtz Equation in Random Media: Well-Posedness and A Priori Bounds

Pembery¹,

Spence²

2020

SIAM/ASA J. Uncertainty Quantification

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We prove well-posedness results and a priori bounds on the solution of the Helmholtz equation ∇ · (A∇u) + k 2 nu = −f , posed either in R d or in the exterior of a star-shaped Lipschitz obstacle, for a class of random A and n, random data f , and for all k > 0. The particular class of A and n and the conditions on the obstacle ensure that the problem is nontrapping almost surely. These are the first well-posedness results and a priori bounds for the stochastic Helmholtz equation for arbitrarily large k and for A and n varying independently of k. These results are obtained by combining recent bounds on the Helmholtz equation for deterministic A and n and general arguments (i.e. not specific to the Helmholtz equation) presented in this paper for proving a priori bounds and well-posedness of variational formulations of linear elliptic stochastic PDEs. We emphasise that these general results do not rely on either the Lax-Milgram theorem or Fredholm theory, since neither are applicable to the stochastic variational formulation of the Helmholtz equation.

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confidence: 99%

The Helmholtz Equation in Random Media: Well-Posedness and A Priori Bounds

Pembery¹,

Spence²

2020

SIAM/ASA J. Uncertainty Quantification

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A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty

Malenova

Motamed²,

Runborg

et al. 2016

SIAM/ASA J. Uncertainty Quantification

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We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. Although the wave solution, u ε , is highly oscillatory in both physical and stochastic spaces, we provide theoretical arguments and numerical evidence that quantities of interest based on local averages of |u ε | 2 are smooth, with derivatives in the stochastic space uniformly bounded in ε, where ε denotes the short wavelength. This observable related regularity makes the sparse stochastic collocation approach more efficient than Monte Carlo methods. We present numerical tests that demonstrate this advantage.

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Development of Theoretical Framework for Uncertainty-Based Design Problems

Xiu¹

2011

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The public reportmg burd en for th1s collection of mform ation is estimated to average 1 hour per response. includmg the tim e for rev>ewing instruct>ons. searclhing exi sting data so urces. gathering and mmnta1mng the data needed . and co mpleting and rev1ew 1 ng the collection of 1nforma t1 on. Send co mments regarding th1s burden est1m ate or any other aspect o fth1s collection of mformat1on . 1nclud1 ng suggesti ons for reduc1 ng the burden. to the Department of De fense. ExecutiV e Serv1ce D>rectorate (0704 -0 188) Respo ndents should be aware that notwithstanding any other prov1 s1 on of law. no person shall be sub;ect to any penalty for falling to comply w1th a collect> on of 1 nform at1on if 1 t does not display a currently v alid OMB co ntrol number PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION. 1. REPORT DATE (DD-MM-YYYY)12. REPORT TYPE 3. DATES COVERED (From-To) SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)AF Office of Scientific Research, AFOSR 875 N. Randolph St., Room 3112 Arlington, VA 22203 SPONSOR/MONITOR'S REPORT NUMBER(S)AFRL-OSR-VA-TR-2012-0271 DISTRIBUTION/AVAILABILITY STATEMENTDistribution A --Approved for public release SUPPLEMENTARY NOTES ABSTRACTThe major accomplishments include: -Development of a new and more rigorous variability measure for robust optimization -Development of an efficient algorithm for robust optimization -Development of a highly efficient numerical method for computing rare failure probability. It is better than any of the existing methods by several orders.-Development of the first-ever numerical method for epistemic uncertainty analysis. 1S. SUBJECT TERMS

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Fast Method for High-Frequency Acoustic Scattering From Random Scatterers

Cited by 4 publications

References 26 publications

The Helmholtz Equation in Random Media: Well-Posedness and A Priori Bounds

The Helmholtz Equation in Random Media: Well-Posedness and A Priori Bounds

A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty

Development of Theoretical Framework for Uncertainty-Based Design Problems

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