Solving partial differential equations numerically on manifolds with arbitrary spatial topologies

DOI10.1016/j.jcp.2013.02.031zbMath1349.65651arXiv1210.5016OpenAlexW2074038909MaRDI QIDQ347651

Lee Lindblom, Béla Szilágyi

Publication date: 5 December 2016

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

Full work available at URL: https://arxiv.org/abs/1210.5016

zbMATH Keywords

numerical methodspartial differential equationstopological manifolds

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (7)

Integral equation methods for the Yukawa-Beltrami equation on the sphere ⋮ Building three-dimensional differentiable manifolds numerically ⋮ Constructing reference metrics on multicube representations of arbitrary manifolds ⋮ Scalar, vector and tensor harmonics on the three-sphere ⋮ Fast integral equation methods for the Laplace-Beltrami equation on the sphere ⋮ The method of fundamental solutions applied to boundary value problems on the surface of a sphere ⋮ Simple numerical solutions to the Einstein constraints on various three-manifolds

Cites Work

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• The spectral element method for the shallow water equations on the sphere
• A multidomain spectral method for solving elliptic equations
• A family of embedded Runge-Kutta formulae
• The ``cubed sphere: A new method for the solution of partial differential equations in spherical geometry
• Affine structures in 3-manifolds. V: The triangulation theorem and Hauptvermutung
• Multi-block simulations in general relativity: high-order discretizations, numerical stability and applications
• Tensor spherical harmonics on S2 and S3 as eigenvalue problems
• Tensor harmonics on the 3-sphere
• A new generalized harmonic evolution system
• A multi-block infrastructure for three-dimensional time-dependent numerical relativity

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