In this thesis we construct compatible discretizations of Maxwell's equations. We use the term compatible to describe numerical methods for Maxwell's equations which obey many properties of vector Calculus in a discrete setting. Compatible discretizations preserve the exterior Calculus ensuring that the divergence of the curl and the curl of...
We present a novel strategy for minimizing the numerical dispersion error in edge discretizations of the time-domain electric vector wave equation on square meshes based on the mimetic finite difference (MFD) method. We compare this strategy, called M-adaptation, to two other discretizations, also based on square meshes. One is the...