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High‐order discontinuous Galerkin method for time‐domain electromagnetics on geometry‐independent Cartesian meshes

Héctor Navarro‐García, Rubén Sevilla Orcid Logo, Enrique Nadal, Juan José Ródenas

International Journal for Numerical Methods in Engineering, Volume: 122, Issue: 24

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1002/nme.6846

Abstract

In this work we present the Cartesian grid discontinuous Galerkin (cgDG) finite element method, a novel numerical technique that combines the high accuracy and efficiency of a high-order discontinuous Galerkin discretization with the simplicity and hierarchical structure of a geometry-independent Ca...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa58507
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Abstract: In this work we present the Cartesian grid discontinuous Galerkin (cgDG) finite element method, a novel numerical technique that combines the high accuracy and efficiency of a high-order discontinuous Galerkin discretization with the simplicity and hierarchical structure of a geometry-independent Cartesian mesh. The elements that intersect the boundary of the physical domain require special treatment in order to minimize their effect on the performance of the algorithm. We considered the exact representation of the geometry for the boundary of the domain avoiding any nonphysical artifacts. We also define a stabilization procedure that eliminates the step size restriction of the time marching scheme due to extreme cut patterns. The unstable degrees of freedom are eliminated and the supporting regions of their shape functions are reassigned to neighboring elements. A subdomain matching algorithm and an a posterior enrichment strategy are presented. Combining these techniques we obtain a final spatial discretization that preserves stability and accuracy of the standard body-fitted discretization. The method is validated through a series of numerical tests and it is successfully applied to the solution of problems of interest in the context of electromagnetic scattering with increasing complexity.
Keywords: Cartesian grid finite element method, discontinuous Galerkin, Cartesian grid finite element method, high‐order discretization, Maxwell's equations
College: College of Engineering
Funders: Engineering and Physical Sciences Research Council (Grant Number: EP/T009071/1); Ministerio de Ciencia, Innovación y Universidades (Grant Number: FPU17/03993); Ministerio de Economía y Competitividad (Grant Number: DPI2017-89816-R)
Issue: 24