Performance enhancements of Monte Carlo particle tracing algorithms for large, arbitrary geometries
Charles N. Zeeb, Patrick J. Burns · 1999
Drawing on techniques used in the computer graphics field of ray tracing, an efficient algorithm for tracing particles in large, arbitrary geometries containing nonparticipating media is presented. An efficient intersection algorithm for arbitrary triangles and/or convex planar quadrilaterals is discussed in detail. Several techniques used in ray trac-ing to limit the number of surfaces tested are discussed and the method of uniform spatial division (USD) is implemented. The “mailbox ” tech-nique is also covered. To determine the efficiency of the intersection algorithm, and USD, timing results are presented for a number of dif-ferent spatial divisions for four geometries containing between one thousand and five thousand surfaces each. For USD, speedups in trac-ing time exceeding a factor of eighty are observed. The main focus of this paper is the modeling of complex geome-tries using the Monte Carlo method. Most published radiative Monte Carlo work employ simple geometries such as slabs and cubes; there are few published routines to handle arbitrary, complex geometries. Chin et al. (1989; 1992) have covered several Monte Carlo issues, par-ticularly applying Monte Carlo to finite element meshes. Farmer (1995) has also discussed using Monte Carlo to simulate arbitrary geometries constructed using finite element meshes. In addition, Henson et al. (1996) do discuss some techniques for improving the speed of Monte Carlo routines. Several generalized radiative Monte Carlo programs do exist, for example, TSS (Panczak, 1989) and MATRAD (Koeck, 1988). Still, except for the above references, we have found nothing published about these and other such codes ’ algorithms.