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Numerical homogenization of the acoustic wave equations with a continuum of scales

Owhadi, Houman and Zhang, Lei (2008) Numerical homogenization of the acoustic wave equations with a continuum of scales. Computer Methods in Applied Mechanics and Engineering, 198 (3-4). pp. 397-406. ISSN 0045-7825. doi:10.1016/j.cma.2008.08.012.

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In this paper, we consider numerical homogenization of acoustic wave equations with heterogeneous coefficients, namely, when the bulk modulus and the density of the medium are only bounded. We show that under a Cordes type condition the second order derivatives of the solution with respect to harmonic coordinates are L^2 (instead H^-1 with respect to Euclidean coordinates) and the solution itself is in L∞(0,T,H^2(Ω)) (instead of L∞(0,T,H^1(Ω)) with respect to Euclidean coordinates). Then, we propose an implicit time stepping method to solve the resulted linear system on coarse spatial scales, and present error estimates of the method. It follows that by pre-computing the associated harmonic coordinates, it is possible to numerically homogenize the wave equation without assumptions of scale separation or ergodicity.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Owhadi, Houman0000-0002-5677-1600
Zhang, Lei0000-0001-9031-4318
Additional Information:© 2008 Elsevier. Received 12 November 2007; revised 1 June 2008; accepted 15 August 2008. Available online 2 September 2008. We thank the anonymous referee for valuable comments on our draft.
Subject Keywords:Multi-scale problem; Compensation; Numerical homogenization; Upscaling; Acoustic wave equation
Issue or Number:3-4
Record Number:CaltechAUTHORS:OWHcmame08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12939
Deposited By: Archive Administrator
Deposited On:11 Jan 2009 06:01
Last Modified:08 Nov 2021 22:34

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