A Convergent Point Integral Method for Isotropic Elliptic Equations on a Point Cloud
From MaRDI portal
Publication:5298144
DOI10.1137/15M102592XzbMath1352.65437arXiv1506.03606MaRDI QIDQ5298144
Publication date: 13 December 2016
Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1506.03606
Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)
Related Items
Image colorization based on a generalization of the low dimensional manifold model, Generalization of the weighted nonlocal Laplacian in low dimensional manifold model, Convergence of the Weighted Nonlocal Laplacian on Random Point Cloud, Numerical investigations on trace finite element methods for the Laplace-Beltrami eigenvalue problem, Weighted nonlocal Laplacian on interpolation from sparse data, Monotone meshfree methods for linear elliptic equations in non-divergence form via nonlocal relaxation, Spectral methods for solving elliptic PDEs on unknown manifolds, Ghost Point Diffusion Maps for Solving Elliptic PDEs on Manifolds with Classical Boundary Conditions, Approximating solutions of linear elliptic PDE's on a smooth manifold using local kernel, Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds, CURE: Curvature Regularization for Missing Data Recovery, Harmonic Extension on The Point Cloud, Point Integral Method for Elliptic Equations with Variable Coefficients on Point Cloud, Low Dimensional Manifold Model for Image Processing, Analysis of $p$-Laplacian Regularization in Semisupervised Learning
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A local mesh method for solving PDEs on point clouds
- A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion
- The surface finite element method for pattern formation on evolving biological surfaces
- A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant
- Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches
- Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method
- Modeling and computation of two phase geometric biomembranes using surface finite elements
- A coupled arbitrary Lagrangian-Eulerian and Lagrangian method for computation of free surface flows with insoluble surfactants
- A grid based particle method for moving interface problems
- An Eulerian formulation for solving partial differential equations along a moving interface
- A simple embedding method for solving partial differential equations on surfaces
- From graph to manifold Laplacian: the convergence rate
- A Convergent Adaptive Finite Element Algorithm for Nonlocal Diffusion and Peridynamic Models
- Solving Partial Differential Equations on Point Clouds
- Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
- The Implicit Closest Point Method for the Numerical Solution of Partial Differential Equations on Surfaces
- Spectral convergence of the connection Laplacian from random samples
- Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
- Low Dimensional Manifold Model for Image Processing
- Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
- Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
- A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
- Point Integral Method for Solving Poisson-Type Equations on Manifolds from Point Clouds with Convergence Guarantees
- A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models
- Finite element methods for surface PDEs
- Learning Theory
- Learning Theory
- Variational problems and partial differential equations on implicit surfaces
