Hybrid-Delta Tracking on a Structured Mesh in MCATK

Monte Carlo Application Toolkit (MCATK) commonly uses surface tracking on a structured mesh to compute scalar fluxes. In this mode, higher fidelity requires more mesh cells and isotopes and thus more computational overhead -- since every time a particle changes cells, new cross-sections must be found for all materials in a given cell -- even if no collision occurs in that cell. We implement a hybrid version of Woodcock (delta) tracking on this imposed mesh to alleviate the number of cross-section lookups. This algorithm computes an energy-dependent microscopic majorant cross section is computed for the problem. Each time a particle enters a new cell, rather than computing a true macroscopic cross-section over all isotopes in the cell, the microscopic majorant cross-section is simply multiplied by the total number density of the cell to obtain a macroscopic majorant cross-section for the cell. Delta tracking is then performed within that single cell. This increases performance with minimal code changes, speeding up the solve time by a factor of 1.5 -- 1.75 for k-eigenvalue simulations and 1.2 -- 1.6 for fixed source simulations in a series of materially complex criticality benchmarks.