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PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2022-09-25
Divergence Error Based p-Adaptive Discontinuous Galerkin Solution of Time-Domain Maxwell's Equations
By
Apurva Tiwari,

    Dr. Apurva Tiwari

    Department of Aerospace Engineering

    Indian Institute of Technology Bombay

    India

    Homepage

Avijit Chatterjee

    Prof. Avijit Chatterjee

    Department of Aerospace Engineering

    Indian Institute of Technology

    India

    Homepage

Progress In Electromagnetics Research B, Vol. 96, 153-172, 2022
doi:10.2528/PIERB22080403 | Google Scholar

Abstract
⋅A p-adaptive discontinuous Galerkin time-domain method is developed to obtain high-order solutions to electromagnetic scattering problems. A novel feature of the proposed method is the use of divergence error to drive the p-adaptive method. The nature of divergence error is explored, and that it is a direct consequence of the act of discretization is established. Its relation with relative truncation error is formed which enables the use of divergence error as an inexpensive proxy to truncation error. Divergence error is used as an indicator to dynamically identify and assign spatial operators of varying accuracy to substantial regions in the computational domain. This results in a reduced computational cost compared to a comparable discontinuous Galerkin time-domain solution using uniform degree piecewise polynomial bases throughout. Numerical results are presented to show performance of the proposed divergence error based p-adaptive solutions. It is shown that an accuracy similar to that of uniformly higher order solutions is obtained in terms of the scattering width, using fewer degrees of freedom.
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Citation
Apurva Tiwari, and Avijit Chatterjee, "Divergence Error Based p-Adaptive Discontinuous Galerkin Solution of Time-Domain Maxwell's Equations," Progress In Electromagnetics Research B, Vol. 96, 153-172, 2022.
doi:10.2528/PIERB22080403
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