no code implementations • 21 Dec 2020 • Ben Snowball, Sheehan Olver
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles.
Numerical Analysis Numerical Analysis 65N35
1 code implementation • 25 Jun 2019 • Sheehan Olver, Yuan Xu
We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids.
Classical Analysis and ODEs Numerical Analysis Numerical Analysis 42C05, 42C10, 65D15, 65D32
1 code implementation • 13 Feb 2019 • Sheehan Olver, Alex Townsend, Geoff Vasil
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.
Numerical Analysis 65N35
1 code implementation • 25 Sep 2015 • Geoffrey M. Vasil, Keaton J. Burns, Daniel Lecoanet, Sheehan Olver, Benjamin P. Brown, Jeffrey S. Oishi
In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk.
Numerical Analysis Instrumentation and Methods for Astrophysics
3 code implementations • 2 Jul 2015 • Richard Mikael Slevinsky, Sheehan Olver
The resulting system can be solved in ${\cal O}(m^2n)$ operations using an adaptive QR factorization, where $m$ is the bandwidth and $n$ is the optimal number of unknowns needed to resolve the true solution.
Numerical Analysis 65N35, 65R20, 33C45, 31A10
1 code implementation • 20 Oct 2014 • Alex Townsend, Thomas Trogdon, Sheehan Olver
The algorithm is based on Newton's method with carefully selected initial guesses for the nodes and a fast evaluation scheme for the associated orthogonal polynomial.
Numerical Analysis
2 code implementations • 12 Jun 2014 • Richard Mikael Slevinsky, Sheehan Olver
We investigate the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods.
Numerical Analysis 30C30, 41A30, 65D30, 65L10
