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Since 2019, Matheon's application-oriented mathematical research activities are being continued in the framework of the Cluster of Excellence MATH+
www.mathplus.de
The Matheon websites will not be updated anymore.

Dr. Faniry Razafindrazaka

Faniry.Razafi@fu-berlin.de


Projects as a member

  • CH18

    Boundary-Sensitive Hodge Decompositions

    Prof. Dr. Konrad Polthier

    Project heads: Prof. Dr. Konrad Polthier
    Project members: Dr. Faniry Razafindrazaka
    Duration: 01.06.2017 - 31.12.2019
    Status: running
    Located at: Freie Universität Berlin

    Description

    Based on novel results for smooth and discrete Hodge-type decompositions on manifolds with boundary, this project aims to incorporate discrete boundary-sensitive Hodge decompositions as a central tool for the analysis of blood flow and parameterization of blood vessels. These decompositions provide the following two substantial improvements over existing methods: first, they are able to distinguish harmonic blood flow arising from boundary in- and out ow from harmonic circulations induced by the interior topology of the geometry. Second, they guarantee a theoretically-sound linkage of certain fields with controlled boundary behaviour to cohomological quantities of the geometry, which is the essential and still missing ingredient for the creation of periods to ensure global matching of parameter lines in modern parameterization techniques.

    http://www.mi.fu-berlin.de/en/math/groups/ag-geom/projects/ch18/index.html

Projects as a guest