This work is concerned with the numerical treatment of the system of three-dimensional frequency-domain (or time-harmonic) Maxwell equations using a high order hybridizable discontinuous Galerkin (HDG) approximation method combined with domain decomposition (DD) on the basis of hybrid iterative-direct parallel solution strategies. The proposed HDG method preserves the advantages of classical DG methods previously introduced for the time-domain Maxwell equations, in particular, in terms of accuracy and flexibility with regards to the discretization of complex geometrical features, while keeping the computational efficiency at the level of the reference edge element-based finite element formulation widely adopted for the considered PDE system. We study in details the computational performances of the resulting DD solvers in particular in terms of scalability metrics by considering both a model test problem and more realistic large-scale simulations performed on high performance computing systems consisting of networked multicore nodes. KEYWORDScomputational electromagnetics, domain decomposition, frequency-domain Maxwell equations, high performance computing, hybridizable discontinuous Galerkin *https://www.ansys.com/products/electronics/ansys-hfss † https://www.comsol.com Int J Numer Model. 2020;33:e2678. wileyonlinelibrary.com/journal/jnm

In this paper, we present an overview of our innovative computational methodology based on statistical learning optimization to optimize highly efficient and robust metasurface designs. We have optimized highly efficient single-and multi-functional devices. In addition, we have extended our multi-objective optimization to account for manufacturing imperfections.

The discontinuous Galerkin (DG) method is a general numerical modeling approach that has been extensively studied in the last 20 years for the solution of many systems of partial differential equations in physics. Its development for the numerical treatment of the system of Maxwell equations was initiated by the applied mathematics community in the early 2000s. It is now a very popular method for time-domain electromagnetics, which is increasingly used and further developed by the applied physics and electrical engineering communities. More recently, a specific variant of DG, referred to as hybridized DG (or HDG), has been proposed for frequency-domain electromagnetics. DG methods possess nice features that make them particularly attractive for dealing with heterogeneous media and irregularly shaped or curved geometries, and more generally with multiscale problems. Not surprisingly, the method has also been adopted by researchers in the nano-optics field. In this paper, we report on our recent efforts for extending the capabilities of this family of methods for the numerical modeling of nanoscale light-matter interactions.

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