A sparse spectral method on triangles
File(s)
Accepted version
Author(s)
Olver, Sheehan
Townsend, Alex
Vasil, Geoffery
Type
Journal Article
Abstract
In this paper, we demonstrate that many of the computational tools for univariate
orthogonal polynomials have analogues for a family of bivariate orthogonal polynomials on the triangle, including Clenshaw’s algorithm and sparse differentiation operators. This allows us to derive
a practical spectral method for solving linear partial differential equations on triangles with sparse
discretizations. We can thereby rapidly solve partial differential equations using polynomials with
degrees in the thousands, resulting in sparse discretizations with as many as several million degrees
of freedom.
orthogonal polynomials have analogues for a family of bivariate orthogonal polynomials on the triangle, including Clenshaw’s algorithm and sparse differentiation operators. This allows us to derive
a practical spectral method for solving linear partial differential equations on triangles with sparse
discretizations. We can thereby rapidly solve partial differential equations using polynomials with
degrees in the thousands, resulting in sparse discretizations with as many as several million degrees
of freedom.
Date Issued
2019-11-21
Date Acceptance
2019-08-29
Citation
SIAM Journal on Scientific Computing, 2019, 41 (6), pp.A3728-A3756
ISSN
1064-8275
Publisher
Society for Industrial and Applied Mathematics
Start Page
A3728
End Page
A3756
Journal / Book Title
SIAM Journal on Scientific Computing
Volume
41
Issue
6
Copyright Statement
© 2019, Society for Industrial and Applied Mathematics
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
spectral methods
triangles
sparse matrices
partial differential equations
SOBOLEV SPACES
APPROXIMATION
Numerical & Computational Mathematics
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0802 Computation Theory and Mathematics
Publication Status
Published
Date Publish Online
2019-11-21