Papadopoulos, I.P.A., Gutleb, T. S. orcid.org/0000-0002-8239-2372, Slevinsky, R.M. et al. (1 more author) (2024) Building Hierarchies of Semiclassical Jacobi Polynomials for Spectral Methods in Annuli. SIAM Journal on Scientific Computing, 46 (6). A3448-A3476. ISSN 1064-8275
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Keywords: | semiclassical orthogonal polynomials, multivariate orthogonal polynomials, spectral methods, disk, annulus |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Computation Science & Engineering |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Nov 2024 10:43 |
Last Modified: | 06 Nov 2024 10:44 |
Published Version: | https://epubs.siam.org/doi/10.1137/23M160846X |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/23M160846X |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:219269 |