500 citations · 1.7k across the 46 of their papers we have counts for
7 papers · 1 filter
Rational function approximation with normalized positive denominators
James Chok, Geoffrey M. Vasil
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic a…
Corner cases of the tau method: symmetrically imposing boundary conditions on hypercubes
Keaton J. Burns, Daniel Fortunato, Keith Julien +1
Polynomial spectral methods produce fast, accurate, and flexible solvers for broad ranges of PDEs with one bounded dimension, where the incorporation of general boundary conditions…
A gyroscopic polynomial basis in the sphere
Abram C. Ellison, Keith Julien, Geoffrey M. Vasil
Standard spectral codes for full sphere dynamics utilize a combination of spherical harmonics and a suitableradial basis to represent fluid variables. These basis functions have a…
Improving convergence of volume penalised fluid-solid interactions
Eric W. Hester, Geoffrey M. Vasil, Keaton J. Burns
We analyse and improve the volume-penalty method, a simple and versatile way to model objects in fluid flows. The volume-penalty method is a kind of fictitious-domain method that a…
A sparse spectral method on triangles
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 tria…
Tensor calculus in spherical coordinates using Jacobi polynomials. Part-I: Mathematical analysis and derivations
Geoff Vasil, Daniel Lecoanet, Keaton Burns +2
This paper presents a method for the accurate and efficient computations on scalar, vector and tensor fields in three-dimensional spherical polar coordinates. The methods uses spin…