5 citations · 8 across the 2 of their papers we have counts for
7 papers
Second order gauge invariant discretizations to the Schrödinger and Pauli equations
Snorre Harald Christiansen, Tore Gunnar Halvorsen
We introduce a numerical method, based on finite elements and lattice gauge theory, to compute approximate solutions to Schrödinger and Pauli equations. The crucial geometric prope…
Stability of an upwind Petrov Galerkin discretization of convection diffusion equations
Snorre H. Christiansen, Tore G. Halvorsen, Torquil M. Sørensen
We study a numerical method for convection diffusion equations, in the regime of small viscosity. It can be described as an exponentially fitted conforming Petrov-Galerkin method.…
Simplicial gauge theory on spacetime
Tore Gunnar Halvorsen, Torquil Macdonald Sørensen
We define a discrete gauge-invariant Yang-Mills-Higgs action on spacetime simplicial meshes. The formulation is a generalization of classical lattice gauge theory, and we prove con…
Simplicial gauge theory and quantum gauge theory simulation
Tore Gunnar Halvorsen, Torquil Macdonald Sørensen
We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed fo…
A simplicial gauge theory
Snorre Harald Christiansen, Tore Gunnar Halvorsen
We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consis…
Manifestly gauge invariant discretizations of the Schrödinger equation
Tore Gunnar Halvorsen, Simen Kvaal
Grid-based discretizations of the time dependent Schrödinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done…