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

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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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 122; no. 24; pp. 7632 - 7663
Main Authors: Navarro‐García, Héctor, Sevilla, Rubén, Nadal, Enrique, Ródenas, Juan José
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 30.12.2021
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Subjects:
Algorithms
Cartesian coordinates
Cartesian grid finite element method
discontinuous Galerkin
Discretization
Domains
Electromagnetic scattering
fictitious domain method
Finite element method
Galerkin method
Geometry
high‐order discretization
Mathematical analysis
Maxwell's equations
Shape functions
Structural hierarchy
Time marching
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary: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.
Bibliography:Funding information
Engineering and Physical Sciences Research Council, EP/T009071/1; Ministerio de Ciencia, Innovación y Universidades, FPU17/03993; Ministerio de Economía y Competitividad, DPI2017‐89816‐R
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6846