Formulation and Implementation of Iterative Method for Generating Spatially-Variant Lattices
The use of a matrix-free, memory-efficient approach to generate large-scale spatially variant lattices (SVL) was explored. A matrix-free iterative SVL generation algorithm was formulated and then implemented with a tremendous memory reduction observed. The algorithm consists of solving first-order central finite-differences along the entirety of the problem space point-by-point to obtain the grating phase function Φ([Special character(s) omitted]) to which all desired spatially variant lattice properties are applied to. The algorithm was studied to identify key areas of data and task parallelism to exploit in heterogeneous computing systems consisting of clusters of central processing units (CPU) and graphics processing units (GPU) combinations. A sequential version of the algorithm was implemented in MATLAB to study memory usage; the sequential implementation proved to cut memory usage in the generation of large-scale SVLs when compared to the traditional matrix approach. Some preliminary efforts were made to map the algorithm to a GPU with the use of the Compute Unified Device Architecture (CUDA); these efforts are presented as the basis to improve the scaling problems inherent with traditional matrix approaches.
Fernando Martinez, Manuel, "Formulation and Implementation of Iterative Method for Generating Spatially-Variant Lattices" (2019). ETD Collection for University of Texas, El Paso. AAI13885551.