Finite element approximation of the Laplace–Beltrami operator on a surface with boundary
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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… read more here.
Keywords: surface boundary; finite element; beltrami operator; surface ... See more keywords
Second-kind integral equations for the Laplace-Beltrami problem on surfaces in three dimensions
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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… read more here.
Keywords: second kind; integral equations; laplace beltrami; kind integral ... See more keywords
Analysis of the Finite Element Method for the Laplace–Beltrami Equation on Surfaces with Regions of High Curvature Using Graded Meshes
Sign Up to like & getrecommendations! 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… read more here.
Keywords: finite element; laplace beltrami; using graded; curvature using ... See more keywords
A gyrification analysis approach based on Laplace Beltrami eigenfunction level sets
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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)… read more here.
Keywords: beltrami eigenfunction; surface; gyrification; laplace beltrami ... See more keywords
On the Laplace–Beltrami operator on compact complex spaces
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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… read more here.
Keywords: laplace beltrami; operator; beltrami operator; complex spaces ... See more keywords
Fast Approximation of Laplace‐Beltrami Eigenproblems
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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… read more here.
Keywords: fast approximation; geometry; laplace beltrami; beltrami ... See more keywords