Generalized finite difference schemes with higher order Whitney forms

Finite difference kind of schemes are popular in approximating wave propagation problems finite dimensional spaces. While Yee’s original paper on the method is already from sixties, mathematically there still remains questions which not yet satisfactorily covered. In this paper, we address two issues kind. Firstly, literature scheme constructed separately for each particular type problem. Here, explicitly generalize Yee to a class that covers at large physics field theories. For introduce all characterised Minkowski manifold by (i) pair first order partial differential equations and (ii) constitutive relation couple with Hodge relation. addition, strategy systematically exploit higher Whitney elements Yee-like approaches. This makes interpolation possible both time space. this, show preserve local character relation, say, laws become imposed set points instead ordinary As result, usage forms does compel change actual solution process all. demonstrated simple example.