THESIS
2022
1 online resource (xiii, 46 pages) : illustrations (some color)
Abstract
We propose a simple
1embedding method for computing the eigenvalues and eigen-functions
of the Laplace-Beltrami operator on implicit surfaces. The approach
follows an embedding approach for solving the surface eikonal equation. We
replace the differential operator on the interface with a typical Cartesian differential
operator in the surface neighborhood and an extension operator on an
outer layer of the computational tube. To observe a numerical convergence as
the underlying mesh size approaches zero, we study different choices of the tube
radius in the form of O(Δx
γ) for γ ∈ [0, 1]. Our proposed algorithm is easy to
implement and efficient. We will give some two- and three-dimensional numerical
examples to demonstrate the effectiveness of our proposed approach....[
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We propose a simple
1embedding method for computing the eigenvalues and eigen-functions
of the Laplace-Beltrami operator on implicit surfaces. The approach
follows an embedding approach for solving the surface eikonal equation. We
replace the differential operator on the interface with a typical Cartesian differential
operator in the surface neighborhood and an extension operator on an
outer layer of the computational tube. To observe a numerical convergence as
the underlying mesh size approaches zero, we study different choices of the tube
radius in the form of O(Δx
γ) for γ ∈ [0, 1]. Our proposed algorithm is easy to
implement and efficient. We will give some two- and three-dimensional numerical
examples to demonstrate the effectiveness of our proposed approach.
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