The Experts below are selected from a list of 2916 Experts worldwide ranked by ideXlab platform
Leonid Goubergrits - One of the best experts on this subject based on the ideXlab platform.
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Hodge Decomposition of wall shear stress vector fields characterizing biological flows.
Royal Society open science, 2019Co-Authors: Faniry H. Razafindrazaka, Pavlo Yevtushenko, Konstantin Poelke, Konrad Polthier, Leonid GoubergritsAbstract:A discrete boundary-sensitive Hodge Decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results...
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Hodge Decomposition of the wall shear stress vector fields characterizing biological flows
arXiv: Quantitative Methods, 2018Co-Authors: Faniry H. Razafindrazaka, Pavlo Yevtushenko, Konstantin Poelke, Konrad Polthier, Leonid GoubergritsAbstract:A discrete boundary-sensitive Hodge Decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results for the smooth and discrete Hodge-Morrey-Friedrichs Decomposition on manifolds with boundary and subdivides the WSS vector field into five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary, which are called the center, Neumann and Dirichlet fields. First, an analysis of WSS in several simulated simplified phantom geometries (duct and idealized aorta) was performed in order to understand the impact of the five components. It was shown that the Decomposition is able to distinguish harmonic blood flow arising from the inlet from harmonic circulations induced by the interior topology of the geometry. Finally, a comparative analysis of 11 patients with coarctation of the aorta (CoA) before and after treatment as well as 10 controls patient was done. The study shows a significant difference between the CoA patients and the healthy controls before and after the treatment. This means a global difference between aortic shapes of diseased and healthy subjects, thus leading to a new type of WSS-based analysis and classification of pathological and physiological blood flow.
Konrad Polthier - One of the best experts on this subject based on the ideXlab platform.
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Hodge Decomposition of wall shear stress vector fields characterizing biological flows.
Royal Society open science, 2019Co-Authors: Faniry H. Razafindrazaka, Pavlo Yevtushenko, Konstantin Poelke, Konrad Polthier, Leonid GoubergritsAbstract:A discrete boundary-sensitive Hodge Decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results...
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Hodge Decomposition of the wall shear stress vector fields characterizing biological flows
arXiv: Quantitative Methods, 2018Co-Authors: Faniry H. Razafindrazaka, Pavlo Yevtushenko, Konstantin Poelke, Konrad Polthier, Leonid GoubergritsAbstract:A discrete boundary-sensitive Hodge Decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results for the smooth and discrete Hodge-Morrey-Friedrichs Decomposition on manifolds with boundary and subdivides the WSS vector field into five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary, which are called the center, Neumann and Dirichlet fields. First, an analysis of WSS in several simulated simplified phantom geometries (duct and idealized aorta) was performed in order to understand the impact of the five components. It was shown that the Decomposition is able to distinguish harmonic blood flow arising from the inlet from harmonic circulations induced by the interior topology of the geometry. Finally, a comparative analysis of 11 patients with coarctation of the aorta (CoA) before and after treatment as well as 10 controls patient was done. The study shows a significant difference between the CoA patients and the healthy controls before and after the treatment. This means a global difference between aortic shapes of diseased and healthy subjects, thus leading to a new type of WSS-based analysis and classification of pathological and physiological blood flow.
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identifying vector field singularities using a discrete Hodge Decomposition
VisMath, 2003Co-Authors: Konrad Polthier, Eike PreusAbstract:We derive a Hodge Decomposition of discrete vector fields on polyhedral surfaces, and apply it to the identification of vector field singularities. This novel approach allows us to easily detect and analyze singularities as critical points of corresponding potentials. Our method uses a global variational approach to independently compute two potentials whose gradient respectively co-gradient are rotation-free respectively divergence-free components of the vector field. The sinks and sources respectively vortices are then automatically identified as the critical points of the corresponding scalar-valued potentials. The global nature of the Decomposition avoids the approximation problem of the Jacobian and higher order tensors used in local methods, while the two potentials plus a harmonic flow component are an exact Decomposition of the vector field containing all information.
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VisMath - Identifying Vector Field Singularities Using a Discrete Hodge Decomposition
Mathematics and Visualization, 2003Co-Authors: Konrad Polthier, Eike PreußAbstract:We derive a Hodge Decomposition of discrete vector fields on polyhedral surfaces, and apply it to the identification of vector field singularities. This novel approach allows us to easily detect and analyze singularities as critical points of corresponding potentials. Our method uses a global variational approach to independently compute two potentials whose gradient respectively co-gradient are rotation-free respectively divergence-free components of the vector field. The sinks and sources respectively vortices are then automatically identified as the critical points of the corresponding scalar-valued potentials. The global nature of the Decomposition avoids the approximation problem of the Jacobian and higher order tensors used in local methods, while the two potentials plus a harmonic flow component are an exact Decomposition of the vector field containing all information.
Faniry H. Razafindrazaka - One of the best experts on this subject based on the ideXlab platform.
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Hodge Decomposition of wall shear stress vector fields characterizing biological flows.
Royal Society open science, 2019Co-Authors: Faniry H. Razafindrazaka, Pavlo Yevtushenko, Konstantin Poelke, Konrad Polthier, Leonid GoubergritsAbstract:A discrete boundary-sensitive Hodge Decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results...
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Hodge Decomposition of the wall shear stress vector fields characterizing biological flows
arXiv: Quantitative Methods, 2018Co-Authors: Faniry H. Razafindrazaka, Pavlo Yevtushenko, Konstantin Poelke, Konrad Polthier, Leonid GoubergritsAbstract:A discrete boundary-sensitive Hodge Decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results for the smooth and discrete Hodge-Morrey-Friedrichs Decomposition on manifolds with boundary and subdivides the WSS vector field into five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary, which are called the center, Neumann and Dirichlet fields. First, an analysis of WSS in several simulated simplified phantom geometries (duct and idealized aorta) was performed in order to understand the impact of the five components. It was shown that the Decomposition is able to distinguish harmonic blood flow arising from the inlet from harmonic circulations induced by the interior topology of the geometry. Finally, a comparative analysis of 11 patients with coarctation of the aorta (CoA) before and after treatment as well as 10 controls patient was done. The study shows a significant difference between the CoA patients and the healthy controls before and after the treatment. This means a global difference between aortic shapes of diseased and healthy subjects, thus leading to a new type of WSS-based analysis and classification of pathological and physiological blood flow.
Li-yeng Sung - One of the best experts on this subject based on the ideXlab platform.
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Multigrid Methods Based on Hodge Decomposition for a Quad-Curl Problem
Computational Methods in Applied Mathematics, 2019Co-Authors: Susanne C. Brenner, Jintao Cui, Li-yeng SungAbstract:AbstractIn this paper we investigate multigrid methods for a quad-curl problem on graded meshes. The approach is based on the Hodge Decomposition. The solution for the quad-curl problem is approximated by solving standard second-order elliptic problems and optimal error estimates are obtained on graded meshes. We prove the uniform convergence of the multigrid algorithm for the resulting discrete problem. The performance of these methods is illustrated by numerical results.
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Hodge Decomposition Methods for a Quad-Curl Problem on Planar Domains
Journal of Scientific Computing, 2017Co-Authors: Susanne C. Brenner, Jiguang Sun, Li-yeng SungAbstract:We develop and analyze $$P_k$$ Lagrange finite element methods for a quad-curl problem on planar domains that is based on the Hodge Decomposition of divergence-free vector fields. Numerical results that illustrate the performance of the finite element methods are also presented.
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Hodge Decomposition for two dimensional time harmonic maxwell s equations impedance boundary condition
Mathematical Methods in The Applied Sciences, 2017Co-Authors: Susanne C. Brenner, Joscha Gedicke, Li-yeng SungAbstract:We extend the Hodge Decomposition approach for the cavity problem of two-dimensional time-harmonic Maxwell's equations to include the impedance boundary condition, with anisotropic electric permittivity and sign-changing magnetic permeability. We derive error estimates for a P1 finite element method based on the Hodge Decomposition approach and present results of numerical experiments that involve metamaterials and electromagnetic cloaking. The well-posedness of the cavity problem when both electric permittivity and magnetic permeability can change sign is also discussed. Copyright © 2015 John Wiley & Sons, Ltd.
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Hodge Decomposition for two‐dimensional time‐harmonic Maxwell's equations: impedance boundary condition
Mathematical Methods in the Applied Sciences, 2015Co-Authors: Susanne C. Brenner, Joscha Gedicke, Li-yeng SungAbstract:We extend the Hodge Decomposition approach for the cavity problem of two-dimensional time-harmonic Maxwell's equations to include the impedance boundary condition, with anisotropic electric permittivity and sign-changing magnetic permeability. We derive error estimates for a P1 finite element method based on the Hodge Decomposition approach and present results of numerical experiments that involve metamaterials and electromagnetic cloaking. The well-posedness of the cavity problem when both electric permittivity and magnetic permeability can change sign is also discussed. Copyright © 2015 John Wiley & Sons, Ltd.
Peer-timo Bremer - One of the best experts on this subject based on the ideXlab platform.
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the natural helmholtz Hodge Decomposition for open boundary flow analysis
IEEE Transactions on Visualization and Computer Graphics, 2014Co-Authors: Harsh Bhatia, Valerio Pascucci, Peer-timo BremerAbstract:The Helmholtz-Hodge Decomposition (HHD), which describes a flow as the sum of an incompressible, an irrotational, and a harmonic flow, is a fundamental tool for simulation and analysis. Unfortunately, for bounded domains, the HHD is not uniquely defined, traditionally, boundary conditions are imposed to obtain a unique solution. However, in general, the boundary conditions used during the simulation may not be known known, or the simulation may use open boundary conditions. In these cases, the flow imposed by traditional boundary conditions may not be compatible with the given data, which leads to sometimes drastic artifacts and distortions in all three components, hence producing unphysical results. This paper proposes the natural HHD, which is defined by separating the flow into internal and external components. Using a completely data-driven approach, the proposed technique obtains uniqueness without assuming boundary conditions a priori. As a result, it enables a reliable and artifact-free analysis for flows with open boundaries or unknown boundary conditions. Furthermore, our approach computes the HHD on a point-wise basis in contrast to the existing global techniques, and thus supports computing inexpensive local approximations for any subset of the domain. Finally, the technique is easy to implement for a variety of spatial discretizations and interpolated fields in both two and three dimensions.
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Comments on the "Meshless Helmholtz-Hodge Decomposition"
IEEE transactions on visualization and computer graphics, 2013Co-Authors: Harsh Bhatia, Gregory Norgard, Valerio Pascucci, Peer-timo BremerAbstract:The Helmholtz-Hodge Decomposition (HHD) is one of the fundamental theorems of fluids describing the Decomposition of a flow field into its divergence-free, curl-free, and harmonic components. Solving for the HHD is intimately connected to the choice of boundary conditions which determine the uniqueness and orthogonality of the Decomposition. This article points out that one of the boundary conditions used in a recent paper “Meshless Helmholtz-Hodge Decomposition” [5] is, in general, invalid and provides an analytical example demonstrating the problem. We hope that this clarification on the theory will foster further research in this area and prevent undue problems in applying and extending the original approach.
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The Helmholtz-Hodge Decomposition—A Survey
IEEE transactions on visualization and computer graphics, 2013Co-Authors: Harsh Bhatia, Gregory Norgard, Valerio Pascucci, Peer-timo BremerAbstract:The Helmholtz-Hodge Decomposition (HHD) describes the Decomposition of a flow field into its divergence-free and curl-free components. Many researchers in various communities like weather modeling, oceanology, geophysics, and computer graphics are interested in understanding the properties of flow representing physical phenomena such as incompressibility and vorticity. The HHD has proven to be an important tool in the analysis of fluids, making it one of the fundamental theorems in fluid dynamics. The recent advances in the area of flow analysis have led to the application of the HHD in a number of research communities such as flow visualization, topological analysis, imaging, and robotics. However, because the initial body of work, primarily in the physics communities, research on the topic has become fragmented with different communities working largely in isolation often repeating and sometimes contradicting each others results. Additionally, different nomenclature has evolved which further obscures the fundamental connections between fields making the transfer of knowledge difficult. This survey attempts to address these problems by collecting a comprehensive list of relevant references and examining them using a common terminology. A particular focus is the discussion of boundary conditions when computing the HHD. The goal is to promote further research in the field by creating a common repository of techniques to compute the HHD as well as a large collection of example applications in a broad range of areas.