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Parameterizing Intersecting Surfaces via Invariants
Timon S. Gutleb, Rhyan Barrett, Julia Westermayr +1
We introduce and analyze numerical companion matrix methods for the reconstruction of hypersurfaces with crossings from smooth interpolants given unordered or, without loss of gene…
Atomic Cluster Expansion without Self-Interaction
Cheuk Hin Ho, Timon S. Gutleb, Christoph Ortner
The Atomic Cluster Expansion (ACE) (Drautz, Phys. Rev. B 99, 2019) has been widely applied in high energy physics, quantum mechanics and atomistic modeling to construct many-body i…
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…
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)^{…
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.…