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.
"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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