Subcell S N sweeping for meshes with reentrant cells
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abstract
We first motivate a general submesh sweeping technique that avoids the complications associated with sweeping on meshes with reentrant cells. The scattering sources are constructed on a primary mesh, but sweeps are performed on a submesh that underlies the primary mesh. A critical aspect of this approach is the projection of the submesh sweep solution onto the primary mesh for purposes of calculating the scattering sources. We define this projection for standard discontinuous finite-element (DFEM) methods and lumped DFEM methods, and discuss our reasons for making this definition. We give computational results for linear-discontinuous and lumped linear-discontinuous discretizations on a 1-D primary mesh and submesh that demonstrate the efficacy of our approach in terms of accuracy and preservation of the thick diffusion limit for a simple but highly relevant case.
