Reconstruction of flow domain boundaries from velocity data via multi-step optimization of distributed resistance
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2929 | |
dc.contributor.author | Pártl, Ondřej | |
dc.contributor.author | Wilbrandt, Ulrich | |
dc.contributor.author | Mura, Joaquín | |
dc.contributor.author | Caiazzo, Alfonso | |
dc.date.accessioned | 2022-07-08T13:04:39Z | |
dc.date.available | 2022-07-08T13:04:39Z | |
dc.date.issued | 2022 | |
dc.description.abstract | We reconstruct the unknown shape of a flow domain using partially available internal velocity measurements. This inverse problem is motivated by applications in cardiovascular imaging where motion-sensitive protocols, such as phase-contrast MRI, can be used to recover three-dimensional velocity fields inside blood vessels. In this context, the information about the domain shape serves to quantify the severity of pathological conditions, such as vessel obstructions. We consider a flow modeled by a linear Brinkman problem with a fictitious resistance accounting for the presence of additional boundaries. To reconstruct these boundaries, we employ a multi-step gradient-based variational method to compute a resistance that minimizes the difference between the computed flow velocity and the available data. Afterward, we apply different post-processing steps to reconstruct the shape of the internal boundaries. To limit the overall computational cost, we use a stabilized equal-order finite element method. We prove the stability and the well-posedness of the considered optimization problem. We validate our method on three-dimensional examples based on synthetic velocity data and using realistic geometries obtained from cardiovascular imaging. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9687 | |
dc.identifier.uri | https://doi.org/10.34657/8725 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2929 | |
dc.relation.issn | 2198-5855 | |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | |
dc.subject.other | Brinkmann equation | eng |
dc.subject.other | gradient-based optimization | eng |
dc.subject.other | stabilized finite elements | eng |
dc.subject.other | boundary reconstruction | eng |
dc.title | Reconstruction of flow domain boundaries from velocity data via multi-step optimization of distributed resistance | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 37 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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