Work

An energy stable discontinuous Galerkin time-domain finite element method in optics and photonics

Year: 2023

Type: article

Abstract: In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell’s equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new capabilities of methods of this type are to efficiently model linear and nonlinear effects, for example of Kerr nonlinearities. Energy stable discretizations both at the semi-discrete and the fully discrete levels are presented. In particular, the proposed semi-discrete scheme is optimally convergent in the spatial variable on Cartesian meshes with Qk-type elements, and the fully discrete scheme is conditionally stable with respect to a specially defined nonlinear electromagnetic energy.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2023.100393

Authors: Asad Anees, Lutz Angermann

Institutions: Axcelis Technologies (United States), University of Agriculture Faisalabad, Clausthal University of Technology

Language: English

Topic: Electromagnetic Simulation and Numerical Methods

Subfield: Electrical and Electronic Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,411

Funder: Technische Universität Clausthal