Parallel Computing of Two Numerical Quadratures for an Integral Formulation of Transient Radiation Transport

Parallel computing of the transient radiative transfer process in the three-dimensional homogeneous and nonhomogeneous participating media is studied with an integral equation model. The model can be used for analyzing the ultra-short light pulse propagation within the highly scattering media. Two numerical quadratures are used: the discrete rectangular volume (DRV) method and YIX method. The parallel versions of both methods are developed for one-dimensional and three-dimensional geometries, respectively. Both quadratures achieve good speedup in parallel performance. Because the integral equation model uses very small amount of memory, the parallel computing can take advantage of having each compute node or processor store the full spatial domain information without using the typical domain decomposition parallelism, which will be necessary in other solution methods, e.g., discrete ordinates and finite volume methods, for large scale simulations. The parallel computation is conducted by assigning different portion of the quadrature to different compute node. In DRV method, a variation of the spatial domain decomposition is used. In the case of YIX scheme, the angular quadrature is divided up according to the number of compute nodes, instead of the spatial domain being divided. This parallel scheme minimizes the communications overhead. The only communication needed is at the end of each time step when each node shares the partial integrated result of the current time step with all other compute nodes. The angular quadrature decomposition approach leads to very good parallel efficiency. Two new discrete ordinate sets are used in the YIX angular quadrature and their parallel performances are discussed. One of the discrete ordinates sets, called spherical ring set, is also suitable for use in the conventional discrete ordinates method.