Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
We recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction (cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate esti...
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| Format: | Journal article |
| Language: | English |
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2003
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| _version_ | 1797104863726796800 |
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| author | Capdeboscq, Y Vogelius, MS |
| author_facet | Capdeboscq, Y Vogelius, MS |
| author_sort | Capdeboscq, Y |
| collection | OXFORD |
| description | We recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction (cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate estimates for the size of the inhomogeneities in terms of multiple boundary measurements. As demonstrated by our computational experiments, these estimates are significantly better than previously known (single measurement) estimates, even for moderate volume fractions. |
| first_indexed | 2024-03-07T06:39:32Z |
| format | Journal article |
| id | oxford-uuid:f8c9a171-cfaf-433f-ae3c-c3d1057a299c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:39:32Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:f8c9a171-cfaf-433f-ae3c-c3d1057a299c2022-03-27T12:53:07ZOptimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurementsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f8c9a171-cfaf-433f-ae3c-c3d1057a299cEnglishSymplectic Elements at Oxford2003Capdeboscq, YVogelius, MSWe recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction (cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate estimates for the size of the inhomogeneities in terms of multiple boundary measurements. As demonstrated by our computational experiments, these estimates are significantly better than previously known (single measurement) estimates, even for moderate volume fractions. |
| spellingShingle | Capdeboscq, Y Vogelius, MS Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements |
| title | Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements |
| title_full | Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements |
| title_fullStr | Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements |
| title_full_unstemmed | Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements |
| title_short | Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements |
| title_sort | optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements |
| work_keys_str_mv | AT capdeboscqy optimalasymptoticestimatesforthevolumeofinternalinhomogeneitiesintermsofmultipleboundarymeasurements AT vogeliusms optimalasymptoticestimatesforthevolumeofinternalinhomogeneitiesintermsofmultipleboundarymeasurements |