Interpolation Type Schemes Application to Analysis of Electromagnetic Field Propagation

Finite Difference Time Domain (FDTD) seems to be a standard approach used in simulation of electromagnetic problems. At the same time, there is a family of interpolation methods, so-called constrained interpolation profile (CIP) methods which have been developed as a numerical solver for multi-dimensional and multi-phase problems not so far. CIP method containes an extended upwind's scheme stencil. Both values of unknown function and it's first derivative (gradient) are considered at the same grid nodes as point values. So, such type of interpolation is nothing but Hermite type interpolation. This allows one to construct a higher-order schemes including the higher order derivatives. Such a numerical tool makes possible analyze electromagnetic field propagation and compare it with the FDTD approach.