A short proof that sweeping is always possible for a spatial discretization with regular triangles and no hanging nodes
This provides a theoretical guarantee for a common numerical method in neutron transport, removing a potential obstacle in mesh generation.
The paper proves that for spatial discretizations using regular triangles without hanging nodes, a sweeping ordering always exists for solving the discrete ordinates equation, ensuring the flow of information is obeyed.
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.