Common Themes in Multi-block Structured Quad/Hex Mesh Generation

The automatic generation of structured multi-block quadrilateral (quad) and hexahedral (hex) meshes has been researched for many years without definitive success. The core problem in quad / hex mesh generation is the placement of mesh singularities to give the desired mesh orientation and distribution [1]. It is argued herein that existing approaches (medial axis, paving / plastering, cross / frame fields) are actually alternative views of the same concept. Using the information provided by the different approaches provides additional insight into the problem.

Channelled Waves in Anisotropic Mesh Metamaterials

Channelled waves in 2-D periodic anisotropic L-C mesh metamaterials have been investigated. Circuit simulation and the newly developed analytical model of a unit cell have demonstrated full qualitative agreement for both lossless and lossy cases. Isofrequencies for a lattice unit cell and the circuit simulations of finite meshes have shown that propagating waves are channelled from a point source as pencil beams which can travel only along specific trajectories. The beam direction varies with frequency, and at the resonance frequency, the phase and group velocities of the travelling wave are orthogonal. The effect of losses was explored, and it was shown that losses cause qualitative changes of the channelled wave type. It was proven that the channelled waves do not follow the laws of geometrical optics (Snell's law, specular reflection, etc.) at the interfaces of L-C meshes but are governed by the conditions of phase synchronism and impedance matching. Only in the special case of dual L-C and C-L meshes with the interface parallel to the axis of rectangular grid excited at the resonance frequency (X=1) do the channels follow the trajectories of optical rays. A planar mesh test cell has been designed and used for retrieving the unit cell L-C parameters from the S-parameter measurements.