Spectral numerical exterior calculus methods for differential equations on radial manifolds

DOI10.1007/s10915-017-0617-2zbMath1404.65225arXiv1703.00996OpenAlexW3099151821MaRDI QIDQ1668714

B. J. Gross, Paul J. Atzberger

Publication date: 29 August 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.00996

zbMATH Keywords

manifoldsnumerical methodspartial differential equationsLaplace-Beltrami

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Hodge theory in global analysis (58A14) Exterior differential systems (Cartan theory) (58A15) Numerical quadrature and cubature formulas (65D32)

Related Items (4)

Coarse-grained methods for heterogeneous vesicles with phase-separated domains: elastic mechanics of shape fluctuations, plate compression, and channel insertion ⋮ A shallow physics-informed neural network for solving partial differential equations on static and evolving surfaces ⋮ Spectral methods for solving elliptic PDEs on unknown manifolds ⋮ Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: a generalized moving least-squares (GMLS) approach

Uses Software

• SymPy
• SHTns

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spherical harmonics and approximations on the unit sphere. An introduction
• The chain collocation method: a spectrally accurate calculus of forms
• Manifolds, tensor analysis, and applications.
• Computing Fourier transforms and convolutions on the 2-sphere
• FFTs for the 2-sphere-improvements and variations
• Hyperinterpolation on the sphere at the minimal projection order
• A quadrature formula for the sphere of the 131st algebraic order of accuracy
• Polynomial interpolation and hyperinterpolation over general regions
• Constructive polynomial approximation on the sphere
• On the geometric character of stress in continuum mechanics
• Regularized Least Squares Approximations on the Sphere Using Spherical Designs
• Finite element exterior calculus, homological techniques, and applications
• Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms
• Finite element exterior calculus: from Hodge theory to numerical stability
• Quadratures on a sphere
• Isogeometric Analysis
• Finite Element Exterior Calculus for Evolution Problems
• GEOMETRIC ASPECTS OF CURRENTS AND DISTRIBUTIONS
• How good can polynomial interpolation on the sphere be?

This page was built for publication: Spectral numerical exterior calculus methods for differential equations on radial manifolds