collaborators

5 papers

math.NA2024

A sparse hierarchical -finite element method on disks and annuli

Ioannis P. A. Papadopoulos, Sheehan Olver

We develop a sparse hierarchical -finite element method (-FEM) for the Helmholtz equation with variable coefficients posed on a two-dimensional disk or annulus. The mesh is…

math.NA2024

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…

math.NA2023

A frame approach for equations involving the fractional Laplacian

Ioannis P. A. Papadopoulos, Timon S. Gutleb, José A. Carrillo +1

Exceptionally elegant formulae exist for the fractional Laplacian operator applied to weighted classical orthogonal polynomials. We utilize these results to construct a solver, bas…

math.NA2023

Explicit fractional Laplacians and Riesz potentials of classical functions

Timon S. Gutleb, Ioannis P. A. Papadopoulos

We prove and collect numerous explicit and computable results for the fractional Laplacian with as well as its whole space inverse, the Riesz potential, $(-Δ)^{…

math.NA2023

Building hierarchies of semiclassical Jacobi polynomials for spectral methods in annuli

Ioannis P. A. Papadopoulos, Timon S. Gutleb, Richard M. Slevinsky +1

We discuss computing with hierarchies of families of (potentially weighted) semiclassical Jacobi polynomials which arise in the construction of multivariate orthogonal polynomials.…