most commonly adopted for the simulation of light-matter interactions. Most often, commercial simulation software (such as Lumerical FDTD[^1] and Comsol Multiphysics[^2]) is used for that purpose. However, these methods and computer codes do not always offer the required capabilities for addressing accurately and efficiently the complexity of the physical phenomena underlying nanometer scale light-matter interactions. In the academic community, also the DGTD method has recently been considered in this context [@Busch2011; @Viquerat2015; @HuangYQ2016]. In Ref. [@Schmittetal2016], some numerical results are presented for the NHD model using the DGTD method. In the present paper we are employing the HDG method to solve the frequency-domain NHD and GNOR models. The development of accurate and efficient numerical methods for computational nanophotonics is expected to be a long-lasting demand, both because new models are regularly proposed that require innovative numerical methods, and because there is demand for more accurate and faster simulation methods for existing models.

This paper introduces a HDG method for the solution the NHD and GNOR models. The rest of the paper is organized as follows. In section \[sec:models\], we briefly introduce mathematical aspects both of the NHD model and of the GNOR model. HDG formulations are given in section \[sec:hdg\]. 