Journal article
Limiting boundary correctors for periodic microstructures and inverse homogenization series
Inverse problems, v 36(6), p65009
01 Jun 2020
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We consider the two scale asymptotic expansion for a transmission problem modeling scattering by a bounded inhomogeneity with a periodic coefficient in the lower order term of the Helmholtz equation. The squared index of refraction is assumed to be a periodic function of the fast variable, specified over the unit cell with characteristic size epsilon. Since the convergence of the boundary correctors to their limits is in general slow, we explore in detail their use in a second order approximation and show a new convergence estimate for the second order boundary corrector on a square. We show numerical examples of the higher order forward approximation in one and two dimensions. We then use the first order boundary correction as an asymptotic model for inversion and show numerical examples of inversion in the two dimensional case.
Metrics
Details
- Title
- Limiting boundary correctors for periodic microstructures and inverse homogenization series
- Creators
- Fioralba Cakoni - Rutgers, The State University of New JerseyShari Moskow - Drexel UniversityTayler Pangburn - Drexel University
- Publication Details
- Inverse problems, v 36(6), p65009
- Publisher
- Iop Publishing Ltd
- Number of pages
- 27
- Grant note
- CCF-1934924 / NSF HDR TRIPODS award FA9550-20-1-0024 / AFOSR; United States Department of Defense; Air Force Office of Scientific Research (AFOSR) DMS1715425; DMS-1813492 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000540839100001
- Scopus ID
- 2-s2.0-85087544186
- Other Identifier
- 991019167973404721
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
- Physics, Mathematical