13 citations · 36 across the 19 of their papers we have counts for
19 papers
On a semi-discrete model of Maxwell's equations in three and two dimensions
Volodymyr Sushch
In this paper, we develop a geometric, structure-preserving semi-discrete formulation of Maxwell's equations in both three- and two-dimensional settings within the framework of dis…
2D discrete Yang-Mills equations on the torus
Volodymyr Sushch
In this paper, we introduce a discretization scheme for the Yang-Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this fram…
2D discrete Hodge-Dirac operator on the torus
Volodymyr Sushch
We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dira…
Chiral properties of discrete Joyce and Hestenes equations
Volodymyr Sushch
This paper concerns the question of how chirality is realized for discrete counterparts of the Dirac-Kähler equation in the Hestenes and Joyce forms. It is shown that left and righ…
A discrete version of plane wave solutions of the Dirac equation in the Joyce form
Volodymyr Sushch
We construct a discrete version of the plane wave solution to a discrete Dirac-Kähler equation in the Joyce form. A geometric discretisation scheme based on both forward and backwa…
A discrete Dirac-Kähler equation using a geometric discretisation scheme
Volodymyr Sushch
Discrete models of the Dirac-Kähler equation and the Dirac equation in the Hestenes form are discussed. A discrete version of the plane wave solutions to a discrete analogue of the…