Journal article
ON THE HOMOGENIZATION OF A SCALAR SCATTERING PROBLEM FOR HIGHLY OSCILLATING ANISOTROPIC MEDIA
SIAM journal on mathematical analysis, v 48(4), pp 2532-2560
01 Jan 2016
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We study the homogenization of a transmission problem arising in the scattering theory for bounded inhomogeneities with periodic coefficients modeled by the anisotropic Helmholtz equation. The coefficients are assumed to be periodic functions of the fast variable, specified over the unit cell with characteristic size epsilon. By way of multiple scales expansion, we focus on the O(epsilon(k)), k = 1,2, bulk and boundary corrections of the leading-order (O(epsilon)) homogenized transmission problem. The analysis in particular provides the H-1 and L-2 estimates of the error committed by the first order-corrected solution considering (i) bulk correction only and (ii) boundary and bulk correction. We treat explicitly the O(epsilon) boundary correction for the transmission problem when the scatterer is a unit square and show it has an L-2-limit as epsilon -> 0, provided that the boundary cutoff of cells is fixed. We also establish the O(epsilon(2)) bulk correction describing the mean wave motion inside the scatterer. The analysis also highlights a previously established, yet scarcely recognized, fact that the O(epsilon) bulk correction of the mean motion vanishes identically.
Metrics
Details
- Title
- ON THE HOMOGENIZATION OF A SCALAR SCATTERING PROBLEM FOR HIGHLY OSCILLATING ANISOTROPIC MEDIA
- Creators
- Fioralba Cakoni - Rutgers, The State University of New JerseyBojan B. Guzina - Civil, Environmental, and Geo- EngineeringShari Moskow - Drexel University
- Publication Details
- SIAM journal on mathematical analysis, v 48(4), pp 2532-2560
- Publisher
- Siam Publications
- Number of pages
- 29
- Grant note
- FA9550-131-0199 / AFOSR; United States Department of Defense; Air Force Office of Scientific Research (AFOSR) DMS-1602802; DMS1108858; DMS1411721 / NSF; National Science Foundation (NSF) 10-862 / DOE NEUP; United States Department of Energy (DOE)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000385023400009
- Scopus ID
- 2-s2.0-84984999155
- Other Identifier
- 991019167983204721
UN Sustainable Development Goals (SDGs)
This publication has contributed to the advancement of the following goals:
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied