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High‐order discontinuous Galerkin method for time‐domain electromagnetics on geometry‐independent Cartesian meshes
Author(s) -
NavarroGarcía Héctor,
Sevilla Rubén,
Nadal Enrique,
Ródenas Juan José
Publication year - 2021
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6846
Subject(s) - discretization , polygon mesh , discontinuous galerkin method , cartesian coordinate system , galerkin method , mathematics , boundary (topology) , finite element method , regular grid , geometry , algorithm , boundary value problem , mathematical analysis , grid , physics , thermodynamics
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.