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PIER PIER B PIER C PIER M PIER Letters
2015-11-06
The Time-Harmonic Discontinuous Galerkin Method as a Robust Forward Solver for Microwave Imaging Applications
By
Ian Jeffrey,

    Dr. Ian Jeffrey

    Electrical and Computer Engineering

    University of Manitoba

    Canada

    Homepage

Nicholas Geddert,

    Mr. Nicholas Geddert

    Department of Electrical and Computer Engineering

    University of Manitoba

    Canada

    Homepage

Kevin Brown,

    Dr. Kevin Brown

    Department of Electrical and Computer Engineering

    University of Manitoba

    Canada

    Homepage

Joe LoVetri

    Dr. Joe LoVetri

    Department of Electrical and Computer Engineering

    University of Manitoba

    Canada

    Homepage

Progress In Electromagnetics Research, Vol. 154, 1-21, 2015
doi:10.2528/PIER15090403
Abstract
Novel microwave imaging systems require flexible forward solvers capable of incorporating arbitrary boundary conditions and inhomogeneous background constitutive parameters. In this work we focus on the implementation of a time-harmonic Discontinuous Galerkin Method (DGM) forward solver with a number of features that aim to benefit tomographic microwave imaging algorithms: locally varying high-order polynomial field expansions, locally varying high-order representations of the complex constitutive parameters, and exact radiating boundary conditions. The DGM formulated directly from Maxwell's curl equations facilitates including both electric and magnetic contrast functions, the latter being important when considering quantitative imaging with magnetic contrast agents. To improve forward solver performance we formulate the DGM for time-harmonic electric and magnetic vector wave equations driven by both electric and magnetic sources. Sufficient implementation details are provided to permit existing DGM codes based on nodal expansions of Maxwell's curl equations to be converted to the wave equation formulations. Results are shown to validate the DGM forward solver framework for transverse magnetic problems that might typically be found in tomographic imaging systems, illustrating how high-order expansions of the constitutive parameters can be used to improve forward solver performance.
Citation
Ian Jeffrey, Nicholas Geddert, Kevin Brown, and Joe LoVetri, "The Time-Harmonic Discontinuous Galerkin Method as a Robust Forward Solver for Microwave Imaging Applications," Progress In Electromagnetics Research, Vol. 154, 1-21, 2015.
doi:10.2528/PIER15090403
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