R.P. Souto, H.F. de Campos Velho, S. Stephany, E.S. Chalhoub (2002): Performance Analysis of Radiative Transfer Algorithms for Hydrologic Optics, Brazilian Congress on Computing and Applied Mathematics (CNMAC-2002), 11-15 September, Brasil.

Abstract: The computational performance of three algorithms for solving the radiative transfer equation (RTE) were studied: HYDROLIGHT [2], PEESNA [1] and LTSN [3]. These algorithms correspond, respectively to invariant imbedding, analytical discrete-ordinates and LTSn [3] methods. The related codes were used in a Hydrological Optics test case, in order to calculate the surface-emergent radiation intensities (radiances) from the incident radiances. The inherent optical properties are supposed known, as the absorption and the scattering coefficients, and a typical test case of coastal water was chosen. The HYDROLIGHT code is divided in two parts. HYDROLIGHT-1 performs the defined spatial discretization, while HYDROLIGHT-2 can be used as a pre-processing step to calculate the discrete phase function values or to solve the RTE for the given discretization and phase function. Timing and profiling of the three codes was performed but, in the case of HYDROLIGHT, only the time to solve the RTE was considered. PEESNA and LTSN times include phase function calculations. Take in account previous considerations, the HYDROLIGHT-2 code was the fastest, followed by the PEESNA and the LTSN. However, it was also intended to check how suitable are these methods for parallelization. The three codes perform spatial discretization of the domain and Fourier decomposition of the radiances obtaining independent azimuthal modes. Thus an independent RTE can be written for each azimuthal mode and can be assigned to a different processor, in a parallel implementation. In the case of the HYDROLIGHT-2 and LTSN codes, the routines that solve the RTE for each azimuthal mode account for about 90% of the processing time. In the case of the PEESNA code, these calculations are similar to those of the LTSN algorithm, but the related routines account for only 40% of the processing time. However, the sequential version of the PESSNA is about 10 times faster than the LTSN one for the particular test case. Future work points out to sequential optimizations of these codes based on the profiling data [4] and to develop a parallel implementation. The independent calculations in each method suggest that good speed-ups can be achieved with standard parallelization techniques. It is intended to use the MPI message passing communication library and execute the parallelized codes in a distributed memory machine, a multicomputer based on IA-32 architecture.

References:

[1] E.S. Chalhoub, R.D.M. Garcia (2000): The equivalence between two techniques of angular interpolation for the discrete-ordinates method, J. Quant. Spec. & Rad. Transfer, 64, 317-535.

[2] C.D. Mobley (1995): Hydrolight 3.0 user's guide, Menlo Park, USA, SRI Intl.

[3] C.F. Segatto, M.T. Vilhena (1994): Extensions of the LTSn formulation for discrete ordinates problems without azimuthal simmetry, Ann. Nucl. En., 21, 701-710.

[4] S. Stephany, R.V. Correa, C.L. Mendes, A.J. Preto (2000): Identifying Performance Bottlenecks in a Radiative Transfer Application, Application of High Performance Computing in Engineering VI, Edited by M. Ingber, H. Power, C.A. Brebbia, 51-60, by , WIT Press, Southampton, UK.