12 citations · 41 across the 12 of their papers we have counts for
14 papers
Fast automatically differentiable matrix functions and applications in molecular simulations
Tina Torabi, Timon S Gutleb, Christoph Ortner
We describe efficient differentiation methods for computing Jacobians and gradients of a large class of matrix functions including the matrix logarithm and -th roots $…
Modelling power-law ultrasound absorption using a time-fractional, static memory, Fourier pseudo-spectral method
Matthew. J. King, Timon. S. Gutleb, B. E. Treeby +1
We describe and implement a numerical method for modelling the frequency-dependent power-law absorption of ultrasound in tissue, as governed by the first order linear wave equation…
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.…
A static memory sparse spectral method for time-fractional PDEs
Timon S. Gutleb, José A. Carrillo
We introduce a method which provides accurate numerical solutions to fractional-in-time partial differential equations posed on with withou…
Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations
Timon S. Gutleb, Sheehan Olver, Richard Mikael Slevinsky
We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified m…
Computation of Power Law Equilibrium Measures on Balls of Arbitrary Dimension
Timon S. Gutleb, José A. Carrillo, Sheehan Olver
We present a numerical approach for computing attractive-repulsive power law equilibrium measures in arbitrary dimension. We prove new recurrence relationships for radial Jacobi po…
Computing Equilibrium Measures with Power Law Kernels
Timon S. Gutleb, José A. Carrillo, Sheehan Olver
We introduce a method to numerically compute equilibrium measures for problems with attractive-repulsive power law kernels of the form us…
A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels
Timon S. Gutleb
We present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator's banded sparsity structure when acting on specific Jacobi…
A time splitting method for the three-dimensional linear Pauli equation
Timon S. Gutleb, Norbert J. Mauser, Michele Ruggeri +1
We analyze a numerical method to solve the time-dependent linear Pauli equation in three space dimensions. The Pauli equation is a semi-relativistic generalization of the Schröding…
A sparse spectral method for Volterra integral equations using orthogonal polynomials on the triangle
Timon S. Gutleb, Sheehan Olver
We introduce and analyse a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the V…