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PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2016-03-01
Mesh Optimization for Maxwell's Equations with Respect to Anisotropic Materials Using Geometric Algebra
By
Mariusz Klimek,

    Dr. Mariusz Klimek

    Graduate School of Computational Engineering

    Technische Universitaet Darmstadt

    Germany

    Homepage

Sebastian Schops,

    Dr. Sebastian Schops

    Graduate School of Computational Engineering

    Technische Universitat Darmstadt

    Germany

    Homepage

Thomas Weiland

    Dr. Thomas Weiland

    Institut fuer Theorie Elektromagnetischer Felder (TEMF)

    Technische Universitat Darmstadt

    Germany

    Homepage

Progress In Electromagnetics Research M, Vol. 46, 153-163, 2016
doi:10.2528/PIERM15110402 | Google Scholar

Abstract
Clifford's Geometric Algebra provides an elegant formulation of Maxwell's equations in the spacetime setting. Its clear geometric interpretation is used to derive a goal function, whose minimization results in Hodge-optimized material matrices being diagonal or diagonal-dominant. Effectively it is an optimization of the primal/dual mesh pair of a finite difference based discretization scheme taking into account the material properties. As a research example a standing wave in 2D cavity filled with an anisotropic material is investigated. Convergence of the scheme for various choices of mesh pairs is discussed. The limitations of the method in the 3D case are presented.
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Citation
Mariusz Klimek, Sebastian Schops, and Thomas Weiland, "Mesh Optimization for Maxwell's Equations with Respect to Anisotropic Materials Using Geometric Algebra," Progress In Electromagnetics Research M, Vol. 46, 153-163, 2016.
doi:10.2528/PIERM15110402
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