10 papers · 1 filter
A sparse spectral method on a class of domains bounded by planar algebraic curves
Jiajie Yao, Marco Fasondini, Sheehan Olver
We develop a sparse spectral method for solving partial differential equations on a class of two-dimensional geometries bounded by algebraic curves. The numerical method uses gener…
The QR factorization of a banded-plus-semiseparable matrix is computable in linear complexity with Householder reflections
Tao Chen, Sheehan Olver
We show that the QR factorization of a banded-plus-semiseparable (BPS) matrix is computable in optimal linear complexity with respect to the discretization size by showing that the…
Orthogonal polynomials for the de Rham complex on the disk and cylinder
Sheehan Olver
This paper constructs polynomial bases that capture the structure of the de Rham complex with boundary conditions in disks and cylinders (both periodic and finite) in a way that re…
A sparse -finite element method for piecewise-smooth differential equations with periodic boundary conditions
Daniel VandenHeuvel, Sheehan Olver
We develop an efficient -finite element method for piecewise-smooth differential equations with periodic boundary conditions, using orthogonal polynomials defined on circular a…
Quasi-optimal complexity -FEM for the Poisson Equation on a rectangle
Kars Knook, Sheehan Olver, Ioannis P. A. Papadopoulos
We show, in one dimension, that an -Finite Element Method (-FEM) discretisation can be solved in optimal complexity because the discretisation has a special sparsity struct…
Parallelisation of partial differential equations via representation theory
Sheehan Olver
Incorporating symmetries into the numerical solution of differential equations has been a mainstay of research over the last 40 years, however, one aspect is less known and under-u…