A non-conformal domain decomposition method utilizing rotating subdomains and non-matching grids for periodic metamaterial simulation

Abstract

Electromagnetic metamaterials possess characteristics such as having large-scale, periodic, multi-media, and complex geometric structures, making them highly suitable for simulation using the finite element domain decomposition method (DDM). This work proposes a non-conformal DDM for simulating finite-period metamaterials, achieving simulation with a minimal number of domains while significantly reducing computational resource consumption. First, the computational domain of the periodic metamaterial is partitioned into several non-conformal hexahedral subdomains. Subsequently, a limited number of non-repetitive subdomain models with non-matching grids are constructed, leveraging the three-dimensional rotational and translational properties of these subdomains to facilitate simulation. By eliminating the necessity to construct models for every subdomain, a substantial reduction in memory consumption is achieved. Second, an iteration method for solving the matrix equations of subdomains is enhanced by introducing a multifrontal block incomplete Cholesky decomposition preconditioner, thereby enhancing the computational efficiency of matrix equations with a large number of unknowns. Meanwhile, parallel computing techniques are employed to accelerate the proposed method. Finally, we integrate the aforementioned method into a solver and leverage it to develop an electromagnetic simulation tool tailored for metamaterials. The tool is employed to simulate metamaterial structures of varying scales, resulting in notable reductions in both memory and time consumption while maintaining accuracy comparable to commercial software.