A short proof that sweeping is always possible for a spatial discretization with regular triangles and no hanging nodes

TL;DR

This paper proves that for a spatial discretization using regular triangles without hanging nodes, an ordering for the sweeping procedure in neutron transport calculations always exists, ensuring efficient explicit solutions.

Contribution

It provides a rigorous proof that sweeping is always possible under specific mesh conditions, improving understanding of discretization strategies for neutron transport.

Findings

Sweeping order can always be found for regular triangular meshes without hanging nodes.

The proof guarantees the applicability of explicit solution methods in these discretizations.

This result supports the use of such meshes in neutron transport simulations.

Abstract

Sweeping is a commonly used procedure to explicitly solve the discrete ordinates equation, which itself is a common approximation of the neutron transport equation. To sweep through the computational domain, an ordering of the spatial cells is required that obeys the flow of information. We show that this ordering can always be found, assuming a discretization of the spatial domain with regular triangles with no hanging nodes.