Building hierarchies of semiclassical Jacobi polynomials for spectral methods in annuli
File(s)
Accepted version
Author(s)
Papadopoulos, Ioannis
Gutleb, Timon
Slevinsky, Mikael
Olver, Sheehan
Type
Journal Article
Abstract
We discuss computing with hierarchies of families of (potentially weighted) semiclassical Jacobi polynomials which arise in the construction of multivariate orthogonal polynomials. In particular, we outline how to build connection and differentiation matrices with optimal complexity and compute analysis and synthesis operations in quasi-optimal complexity. We investigate a particular application of these results to constructing orthogonal polynomials in annuli, called the generalized Zernike annular polynomials, which lead to sparse discretizations of partial differential equations (PDEs). We compare against a scaled-and-shifted Chebyshev–Fourier series showing that in general the annular polynomials converge faster when approximating smooth functions and have better conditioning. We also construct a sparse spectral element method by combining disk and annulus cells, which is highly effective for solving PDEs with radially discontinuous variable coefficients and data.
Date Issued
2024-12-01
Date Acceptance
2024-07-17
Citation
SIAM Journal on Scientific Computing, 2024, 46 (6), pp.A3448-A3476
ISSN
1064-8275
Publisher
Society for Industrial and Applied Mathematics
Start Page
A3448
End Page
A3476
Journal / Book Title
SIAM Journal on Scientific Computing
Volume
46
Issue
6
Copyright Statement
© 2024 Society for Industrial and Applied Mathematics. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published
Date Publish Online
2024-11-05