*2.1.1 Structure data sampling*

The hexahedral meshing algorithm is used within time-domain MWS solver to generate mesh cells adapted to material and geometric properties to represent the input structure and background space. MWS solves and establishes the near-field distributions on this meshed representation rather than the input structure. Structures such as Vivaldi antennas contain diagonal components in the Vivaldi-curved edges that are not parallel with any of the coordinate axes. This causes a stepped or staircase mesh structure to represent these structural components.

The algorithm in the structural data sampling step extracts the meshing lines and the material matrix data of the whole simulation space from the MWS solver, and it reconstructs the meshed structure of the main elements of the structure for the next sampling and analysis steps. Specifically, based on the material matrix data, the metal cells of the meshed metal patches of the Vivaldi antenna are identified. These cells are merged together into a reconstructed structure of the meshed metal patch. **Figure 1** shows the top surface of a small piece of the reconstructed metal patch with the staircase meshed structure for the Vivaldi edge. The reconstructed structure becomes basic for the field data sampling step.
