The Tensor-Train Mimetic Finite Difference Method for Three-Dimensional Maxwell’s Wave Propagation Equations

We construct a compatible/mimetic method for solving the Maxwell wave propagation equations using the tensor train format to represent the electric and magnetic fields. We combine the space discretization with a staggered-in-time scheme to advance the discrete electric and magnetic fields in time. The resulting method is second-order accurate in time and space and compatible, so the approximation of the magnetic flux field has zero discrete divergence. Using the tensor-train format improves the solver performance by orders of magnitude in terms of CPU time and memory storage. A final set of numerical experiments confirms this expectation.