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In this paper, we propose a numerical method to solve isotropic elliptic equations on point cloud by generalizing the point integral method.
Spectral Graph Theory
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The surface finite element method for pattern formation on evolving biological surfaces
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A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion
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Modelling cell movement and chemotaxis using pseudopod-based feedback
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Analysis and approximation of nonlocal diffusion problems with volume constraints
Q. Du, M. Gunzburger, R. B. Lehoucq, and K. Zhou · 2012
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C. Macdonald and S. Ruuth · 2009
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Manifold models for signals and images
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Nonlocal Diffusion Problems
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Modeling and computation of two phase geometric biomem- branes using surface finite elements
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A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws
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A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models
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A convergent adaptive finite element algorithm for nonlocal diffusion and peridynamic models
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Finite element methods for surface pdes
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A local mesh method for solving pdes on point clouds
R. Lai, J. Liang, and H. Zhao · 2013
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Solving partial differential equations on point clouds
J. Liang and H. Zhao · 2013
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