Kernel multigrid on manifolds
DOI10.1016/j.jco.2024.101900MaRDI QIDQ6649711
Thomas Hangelbroek, Christian Rieger
Publication date: 6 December 2024
Published in: Journal of Complexity (Search for Journal in Brave)
geometric multigridkernel-based Galerkin methodslocalized Lagrange basispartial differential equations on manifold
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Ill-posedness and regularization problems in numerical linear algebra (65F22) Smoothness and regularity of solutions to PDEs (35B65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) PDEs on manifolds (35R01)
Cites Work
- Multiscale RBF collocation for solving PDEs on spheres
- Multicloud: Multigrid convergence with a meshless operator
- Spaces of Besov-Hardy-Sobolev type on complete Riemannian manifolds
- Manifolds, tensor analysis, and applications.
- Iterative solution of large sparse systems of equations. Transl. from the German
- A high-order meshless Galerkin method for semilinear parabolic equations on spheres
- Galerkin approximation for elliptic PDEs on spheres
- Partial differential equations. 1: Basic theory
- Polyharmonic and related kernels on manifolds: interpolation and approximation
- Solving partial differential equations on (evolving) surfaces with radial basis functions
- A novel Galerkin method for solving PDES on the sphere using highly localized kernel bases
- Localized Bases for Kernel Spaces on the Unit Sphere
- Kernel Approximation on Manifolds I: Bounding the Lebesgue Constant
- Kernel Approximation on Manifolds II: The $L_{\infty}$ Norm of the $L_2$ Projector
- Parallel Multilevel Preconditioners
- Introduction to Riemannian Manifolds
- Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds
- A Kernel-Based Meshless Conservative Galerkin Method for Solving Hamiltonian Wave Equations
- A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds
- Finite element methods for surface PDEs
- MGM: A Meshfree Geometric Multilevel Method for Systems Arising from Elliptic Equations on Point Cloud Surfaces
This page was built for publication: Kernel multigrid on manifolds
