  Transmission lines are essential components in various signal and power
distribution systems. In addition to their main use as connecting elements,
transmission lines can also be employed as continuous sensors for the
measurement and detection of external influences such as mechanical strains and
deformations. The measuring principle is based on deformation-induced changes
of the characteristic impedance. Reflections of an injected test signal at
resulting impedance mismatches can be used to infer applied deformations. To
determine the effect of deformations on the characteristic impedance, we
develop a numerical framework that allows us to solve Maxwell's equations for
any desired transmission-line geometry over a wide frequency range. The
proposed framework utilizes a staggered finite-difference Yee method on
non-uniform grids to efficiently solve a set of decoupled partial differential
equations that we derive from the frequency domain Maxwell equations. To test
our framework, we compare simulation results with analytical predictions and
corresponding experimental data. Our results suggest that the proposed
numerical framework is able to capture experimentally observed deformation
effects and may therefore be used in transmission-line-based deformation and
strain sensing applications. Furthermore, our framework can also be utilized to
simulate and study the electromagnetic properties of complex arrangements of
conductor, insulator, and shielding materials.
