A Sparse Spectral Method on Triangles

DOI10.1137/19M1245888zbMath1434.65297arXiv1902.04863OpenAlexW2990035746MaRDI QIDQ5204010

Sheehan Olver, Alex Townsend, Geoffrey M. Vasil

Publication date: 9 December 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.04863

zbMATH Keywords

sparse matricespartial differential equationsspectral methodstriangles

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35)

Related Items (11)

Fast algorithms using orthogonal polynomials ⋮ A gyroscopic polynomial basis in the sphere ⋮ A static memory sparse spectral method for time-fractional PDEs ⋮ Computation of power law equilibrium measures on balls of arbitrary dimension ⋮ Gyroscopic polynomials ⋮ A Stieltjes Algorithm for Generating Multivariate Orthogonal Polynomials ⋮ A Sparse Spectral Method for Volterra Integral Equations Using Orthogonal Polynomials on the Triangle ⋮ Solved and unsolved problems ⋮ A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels ⋮ On symmetrizing the ultraspherical spectral method for self-adjoint problems ⋮ Sparse spectral-Galerkin method on an arbitrary tetrahedron using generalized Koornwinder polynomials

Uses Software

• Matlab
• DLMF
• OPQ
• SingularIntegralEquations
• GitHub
• FastTransforms.jl
• BlockBandedMatrices.jl
• MultivariateOrthogonalPolynomials.jl

Cites Work

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• A fast and well-conditioned spectral method for singular integral equations
• The automatic solution of partial differential equations using a global spectral method
• Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods
• Spectral methods on triangles and other domains
• Approximation and orthogonality in Sobolev spaces on a triangle
• Tensor calculus in polar coordinates using Jacobi polynomials
• Recurrence relations for a family of orthogonal polynomials on a triangle
• Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series
• New shape functions for triangular \(p\)-FEM using integrated Jacobi polynomials
• A Fast and Well-Conditioned Spectral Method
• Spectral Methods
• Bernstein–Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures
• Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle
• Spectral Methods in MATLAB
• Bivariate matrix functions
• Orthogonal Polynomials of Several Variables
• The Tau Method

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