# A hybridizable discontinuous Galerkin method for electromagnetics with a view on subsurface applications

## TL;DR

This paper introduces two hybridizable discontinuous Galerkin (HDG) schemes for solving Maxwell's equations in the time domain, focusing on dielectric and conductive media with applications in subsurface electromagnetics.

## Contribution

The paper develops two novel HDG methods for Maxwell's equations, incorporating conduction effects and electric field hybridization, with detailed convergence and validation studies.

## Key findings

- Both methods achieve optimal convergence rates.
- Numerical results validate the accuracy in dielectric and conductive media.
- The schemes are suitable for subsurface electromagnetic applications.

## Abstract

Two Hybridizable Discontinuous Galerkin (HDG) schemes for the solution of Maxwell's equations in the time domain are presented. The first method is based on an electromagnetic diffusion equation, while the second is based on Faraday's and Maxwell--Amp\`ere's laws. Both formulations include the diffusive term depending on the conductivity of the medium. The three-dimensional formulation of the electromagnetic diffusion equation in the framework of HDG methods, the introduction of the conduction current term and the choice of the electric field as hybrid variable in a mixed formulation are the key points of the current study. Numerical results are provided for validation purposes and convergence studies of spatial and temporal discretizations are carried out. The test cases include both simulation in dielectric and conductive media.