3D to 2D surface mesh parameterization for unstructured transmission line method simulations

Advances in small scale fabrication processes have led to the advent of very thin flexible devices such as flexible RFID tags and smart clothing. In a geometrical sense, these present themselves as curved 2D open surfaces embedded in a 3D domain. When simulating EM behavior on these surfaces at low frequencies, a full 3D field model can become computationally expensive in terms of memory and run times. The objective of this paper is to present a method for applying a 2D unstructured Transmission Line Method (TLM) simulation to open, curved surfaces embedded in a 3D domain, by providing a one-to-one mapping of the geometry to a 2D flat plane The simulation results are then mapped back to the original 3D geometry, negating the need for a full 3D simulation. Further, we demonstrate that if the surface material parameters are altered in the vicinity of high curvature, the proposed method is still effective.