works on
fractional laplacian 1numerical analysis 1orthogonal polynomials 1riesz potential 1spectral methods 1

From the 1 of 4 linked papers with an AI index.

most citedExplicit fractional Laplacians and Riesz potentials of classical functions

2 citations · 2 across the 1 of their papers we have counts for

collaborators

4 papers

math.NA2026★ 2 cited

Explicit fractional Laplacians and Riesz potentials of classical functions

Timon S. Gutleb, Ioannis P. A. Papadopoulos

The paper derives explicit formulas for fractional Laplacians and their inverses (Riesz potentials) applied to classical orthogonal polynomials and Bessel functions, providing conc…

math.NA2025

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.NA2025

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.NA2025

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…