Podowitz, Derek Ian (2013-08). Comparison between Pseudo-Spectral Time Domain and Discrete Dipole Approximation Simulations for Single-scattering Properties of Particles. Master's Thesis.
Thesis
The pseudo-spectral time domain (PSTD) and discrete dipole approximation (DDA) are two of the most popular methods to model the single-scattering properties of ice crystals and aerosols. Both methods solve for Maxwell's equations. The PSTD method uses a Fourier pseudo-spectral method and a finite-difference method to compute the spatial and temporal derivatives of electromagnetic fields. The DDA method uses an electromagnetic integral equation in the frequency domain to calculate the single-scattering properties. We used a spherical model for this study because the analytical solution was given by the Lorenz-Mie theory. Previous studies have found that at refractive indices between 1.2 and 1.5, PSTD computed the single-scattering properties of spherical particles faster for large size parameters, while DDA was more computationally efficient at small size parameters; however, these previous studies did not consider absorptive cases. The purpose of this study was to expand the range of refractive indices to include absorptive cases and to determine which method was more efficient for computing the single-scattering properties of atmospheric particles within set criteria. The PSTD and DDA methods were systematically assessed in this study for 31 different realistic complex refractive indices. Similar to the previous studies, it was found that PSTD was more efficient than DDA for particles with large size parameters. The results in this study were consistent with the previous studies for non-absorptive to moderately absorptive particles. However, for strongly absorptive cases, DDA was more efficient than PSTD at all size parameters for the absorptive particles. It was also determined that the efficiencies of the two methods were dependent on both the real and imaginary parts of the complex refractive index. The significance of this study was to improve our understanding of the capabilities of the PSTD and DDA methods for computing single-scattering properties.
