Far-field light scattering from sub-wavelength wafer patterns using a parallel FETI-DP algorithm

The dual-primal finite-element and interconnecting algorithm (FETI-DP) is efficiently applied in parallel to compute the far-field scattering from a wafer with sub-wavelength patterns. As a nonoverlapping domain decomposition method for solving large-scale problems, the FETI-DP algorithm formulates a global interface problem, whose iterative solution is accelerated by solving a global corner problem. To maintain good parallel scaling efficiency, global communication is minimized by using an iterative classical Gram-Schmidt scheme for the global interface problem and a communication-avoiding approach for the global corner problem. In addition, a preconditioner for the corner system matrix is implemented to improve iterative convergence. After computing the far-field data, digital postprocessing is used to remove the background signal and improve the detection sensitivity of isolated defects.