Solving eigenvalue problems on curved surfaces using the closest point method

DOI10.1016/j.jcp.2011.06.021zbMath1231.65205arXiv1106.4351OpenAlexW2022819931MaRDI QIDQ655077

Steven J. Ruuth, Colin B. Macdonald, Jeremy Brandman

Publication date: 28 December 2011

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.4351

zbMATH Keywords

interpolationalgorithmconvergencenumerical exampleseigenvalueseigenfunctionsLaplace-Beltrami operatorfinite differenceimplicit surfacesclosest point methodsurface computation

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Elliptic equations on manifolds, general theory (58J05) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

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Uses Software

• LAPACK
• ARPACK
• MayaVi
• SciPy
• Mayavi
• VTK
• Stanford 3D Scanning Repository
• Python

Cites Work

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• A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion
• Level set equations on surfaces via the closest point method
• A level-set method for computing the eigenvalues of elliptic operators defined on compact hypersurfaces
• An improvement of a recent Eulerian method for solving PDEs on general geometries
• Eulerian finite element method for parabolic PDEs on implicit surfaces
• An Eulerian formulation for solving partial differential equations along a moving interface
• A simple embedding method for solving partial differential equations on surfaces
• Fourth order partial differential equations on general geometries
• Diffusion maps
• The Implicit Closest Point Method for the Numerical Solution of Partial Differential Equations on Surfaces
• Finite Element Methods on Very Large, Dynamic Tubular Grid Encoded Implicit Surfaces
• LAPACK Users' Guide
• ARPACK Users' Guide
• Barycentric Lagrange Interpolation
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Variational problems and partial differential equations on implicit surfaces

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