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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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last_indexed 2021-12-07T04:15:17Z
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spelling 2021-12-06T16:48:02.6370522 v2 58507 2021-10-28 High‐order discontinuous Galerkin method for time‐domain electromagnetics on geometry‐independent Cartesian meshes b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2021-10-28 CIVL 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. Journal Article International Journal for Numerical Methods in Engineering 122 24 Wiley 0029-5981 1097-0207 Cartesian grid finite element method, discontinuous Galerkin, Cartesian grid finite element method, high‐order discretization, Maxwell&apos;s equations 20 10 2021 2021-10-20 10.1002/nme.6846 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 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) 2021-12-06T16:48:02.6370522 2021-10-28T15:48:11.0286471 College of Engineering Engineering Héctor Navarro‐García 1 Rubén Sevilla 0000-0002-0061-6214 2 Enrique Nadal 3 Juan José Ródenas 4 58507__21636__d88d336fe38b43ab84e825315a2e74ce.pdf 58507.pdf 2021-11-23T09:57:19.4734497 Output 5992958 application/pdf Version of Record true © 2021 The Authors. This is an open access article under the terms of the Creative Commons Attribution License true eng http://creativecommons.org/licenses/by/4.0/
title High‐order discontinuous Galerkin method for time‐domain electromagnetics on geometry‐independent Cartesian meshes
spellingShingle High‐order discontinuous Galerkin method for time‐domain electromagnetics on geometry‐independent Cartesian meshes
Rubén Sevilla
title_short High‐order discontinuous Galerkin method for time‐domain electromagnetics on geometry‐independent Cartesian meshes
title_full High‐order discontinuous Galerkin method for time‐domain electromagnetics on geometry‐independent Cartesian meshes
title_fullStr High‐order discontinuous Galerkin method for time‐domain electromagnetics on geometry‐independent Cartesian meshes
title_full_unstemmed High‐order discontinuous Galerkin method for time‐domain electromagnetics on geometry‐independent Cartesian meshes
title_sort High‐order discontinuous Galerkin method for time‐domain electromagnetics on geometry‐independent Cartesian meshes
author_id_str_mv b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Rubén Sevilla
author2 Héctor Navarro‐García
Rubén Sevilla
Enrique Nadal
Juan José Ródenas
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 122
container_issue 24
publishDate 2021
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.6846
publisher Wiley
college_str College of Engineering
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hierarchy_top_id collegeofengineering
hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
document_store_str 1
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description 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.
published_date 2021-10-20T04:15:14Z
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