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Published in 2019 at "Numerische Mathematik"
DOI: 10.1007/s00211-018-0990-2
Abstract: We develop a finite element method for the Laplace–Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are…
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Keywords:
surface boundary;
finite element;
beltrami operator;
surface ... See more keywords
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Published in 2018 at "Advances in Computational Mathematics"
DOI: 10.1007/s10444-018-9587-7
Abstract: The Laplace-Beltrami problem ΔΓψ = f has several applications in mathematical physics, differential geometry, machine learning, and topology. In this work, we present novel second-kind integral equations for its solution which obviate the need for…
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Keywords:
second kind;
integral equations;
laplace beltrami;
kind integral ... See more keywords
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Published in 2018 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-017-0580-y
Abstract: We derive error estimates for the piecewise linear finite element approximation of the Laplace–Beltrami operator on a bounded, orientable, $$C^3$$C3, surface without boundary on general shape regular meshes. As an application, we consider a problem…
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Keywords:
finite element;
laplace beltrami;
using graded;
curvature using ... See more keywords
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Published in 2021 at "NeuroImage"
DOI: 10.1016/j.neuroimage.2021.117751
Abstract: An accurate measure of the complexity of patterns of cortical folding or gyrification is necessary for understanding normal brain development and neurodevelopmental disorders. Conventional gyrification indices (GIs) are calculated based on surface curvature (curvature-based GI)…
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Keywords:
beltrami eigenfunction;
surface;
gyrification;
laplace beltrami ... See more keywords
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Published in 2019 at "Transactions of the American Mathematical Society"
DOI: 10.1090/tran/7848
Abstract: Let ( X , h ) (X,h) be a compact and irreducible Hermitian complex space of complex dimension v > 1 v>1 . In this paper we show that the Friedrichs extension of both the…
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Keywords:
laplace beltrami;
operator;
beltrami operator;
complex spaces ... See more keywords
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Published in 2018 at "Computer Graphics Forum"
DOI: 10.1111/cgf.13496
Abstract: The spectrum and eigenfunctions of the Laplace‐Beltrami operator are at the heart of effective schemes for a variety of problems in geometry processing. A burden attached to these spectral methods is that they need to…
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Keywords:
fast approximation;
geometry;
laplace beltrami;
beltrami ... See more keywords