Parallel overlapping-domain decomposition FDFD for large-scale complex nanostructures modeling

Abstract: The increasing complexity and scale of photonic and electromagnetic devices demand efficient and accurate numerical solvers. In this work, we develop a parallel overlapping domain decomposition method (DDM) based on the finite-difference frequency-domain (FDFD) formulation to model the electromagnetic response of large-scale complex nanostructures. The global computational domain is partitioned into multiple overlapping subdomains terminated with perfectly matched layers (PMLs), enabling seamless source transfer between adjacent subdomains. A multi-frontal preconditioner is employed to accelerate the iterative solution process, while an OpenMP-based parallel implementation ensures high scalability. Several numerical examples are provided to validate the efficiency and accuracy of the proposed algorithm. The results demonstrate excellent agreement with analytical and commercial COMSOL solutions. Notably, the method achieves up to an order of magnitude reduction in computation time, highlighting its potential as a powerful tool for large-scale photonic and electromagnetic modeling.