Computer visions for the eigenvalue problems of embedded surfaces and plane domains
type: Item
instance of: scholarly article
zbMATH Open document ID: 1265.65228
author: Masaki Jumonji
author: Hajime Urakawa
publication date: 2012-10-04T00:00:00Z
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 6090208
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: Laplacian
zbMATH Keywords: embedded surface
zbMATH Keywords: computer graphics
zbMATH Keywords: finite element method
zbMATH Keywords: numerical results
zbMATH Keywords: eigenfunctions
MaRDI profile type: Publication
full work available at URL: v10157-011-0008-1
OpenAlex ID: W2027823188
cites work: Finite Element-Galerkin Approximation of the Eigenvalues and Eigenvectors of Selfadjoint Problems
cites work: Determination of the modulus of quadrilaterals by finite element methods
cites work: Finite element approximation of 𝐻-surfaces
cites work: Q4656949
cites work: The Eigenvalue Problems for the Laplacian on Compact Embedded Surfaces and Three Dimensional Bounded Domains
cites work: Visualization of the eigenvalue problems of the Laplacian for embedded surfaces and its applications
DOI: 10.2478/V10157-011-0008-1
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title: Computer visions for the eigenvalue problems of embedded surfaces and plane domains
published in: Analele Științifice ale Universității Al. I. Cuza din Iași. Serie Nouă. Matematică
review text: The present paper focuses on the numerical computation and the computer graphics of the eigenvalues and eigenfunctions for the eigenvalue problems of the Laplacian on compact embedded surfaces.NEWLINENEWLINE The first part is an introduction into the nature.NEWLINENEWLINE The second part presents the finite element method for the case of eigenvalues problems defined on a bounded domain \(\Omega\subset{\mathbb R}^{n}\) with piecewise smooth boundary \(\partial\Omega\).NEWLINENEWLINE The third part concerns the numerical results of eigenfunctions. One shows the computer graphics for the eigenvalue problems of the Laplacian on compact embedded surfaces: unit sphere, the embedded torus and the dumbells, comparing the exact eigenvalues with the numerical results.NEWLINENEWLINE The fourth section presents the variation of the eigenvalues by deforming either the distance between the centers or the radii, giving also the numerical results.NEWLINENEWLINE Some main observations are within the fifth section.
reviewed by: Romulus Militaru
description: scientific article; zbMATH DE number 6090208