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Showing 1 to 11 of 11 for “"Laplace-Beltrami"”.
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Computing Eigenmodes of Elliptic Operators on Manifolds Using Radial Basis Functions
… methods is proposed to obtain eigenmodes of Laplace-Beltrami operator on manifolds, and its performance is compared against existing alternative methods. Radial Basis Function (RBF)-based methods allow one to obtain interpolation and differentiation matrices easily by using scattered data …
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Steklov geometry processing : an extrinsic approach to spectral shape analysis
… Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many previous extrinsic methods lack theoretical justification. Instead, we consider the Steklov eigenvalue problem, computing the spectrum of the …
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Shape Analysis Using Spectral Geometry
… these challenging problems, we investigate Laplace-Beltrami shape spectra from the differential geometry perspective, focusing more on the intrinsic properties. In this dissertation, the shapes are represented with 2 manifolds, which are differentiable.</p> <p>First, we discuss in detail …
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Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation
… same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate …
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The noncommutative geometry of ultrametric cantor sets
… is then taken further and an analogue of the Laplace-Beltrami operator is created for an ultrametric Cantor set. The Laplacian then allows to create an analogue of Brownian motion generated by this Laplacian. All these tools are then applied to the triadic Cantor set. Other examples of …
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Numerik für die Marangoni-Konvektion beim Floating-Zone Verfahren
… <br>Krümmung durch partielle Integration des Laplace-Beltrami-Operators auf dem <br>freien Rand beruht. Den Abschluss der Arbeit bilden einige numerische Resultate <br>in zwei und drei Raumdimensionen.
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CLASSIFICATION RESULTS FOR SEMILINEAR ELLIPTIC EQUATIONS
… it is proved that the Neumann eigenvalues of the Laplace Beltrami operator on D play a role in computing the Morse index. The second one is about a similar breaking of symmetry result, obtained for positive solutions of the critical Neumann problem in the whole unbounded cone. In this case, it is …
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A posteriori error estimates for the Poisson problem on closed, two-dimensional surfaces
… curved surface, the Poisson Problem features the Laplace-Beltrami Operator, which is a generalization of the Laplacian and specific to the surface where the problem is being solved. A Finite Element Method for solving the Poisson Problem on a closed surface has been described and shown to converge …
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Nodal geometry of eigenfunctions on smooth manifolds and hardy-littlewood-sobolev inequalities on the heisenberg group
… on M:</p> <p>-Δu=Λu,</p> <p>in which Δ is the Laplace-Beltrami operator. That is, u is an eigenfunction with eigenvalue Λ. We analyze the asymptotic behavior of eigenfunctions as Λ go to ∞ (i.e., limit of high energy states) in terms of the following aspects.</p> <p>(1) Local and global …
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Geometric Computing beyond the Laplacian
The Laplace–Beltrami operator, or, Laplacian, is the central object of study in shape analysis, geometry processing, and scientific computing. Motivated by the ubiquity of Laplacian in geometric computing algorithms, this thesis initiates a program for systematically designing novel algorithms by …
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Global Existence of solutions to Reaction-Diffusion Systems with Mass Transport type Boundary Conditions
We consider coupled reaction-diffusion models, where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We proved if vector fields are locally Lipschitz functions and satisfies …