Meshing Operations for SBR+

Surface Curvature Information, Curvilinear Meshing, and Curvature Extraction

When faceted formats such as STL are imported into HFSS, each triangle of the faceted model is flat. Faceted models lack intrinsic curvature information. In order to support methodology features of SBR+ that depend on surface curvature information, such as the ray-tube divergence correction and creeping wave enhancement, local curvature is automatically synthesized (estimated) during SBR+ simulation according to spatial orientation relationships among the immediate neighbors of each flat facet, a process known as curvature extraction.

Unless disabled by the user, curvature extraction is applied to all faceted surfaces. Smooth curvature will be extracted under the assumption of smooth curved surfaces extending across the facet edges. For this extraction process to work well, clean imported STL models satisfying the following criteria are required:

• Two adjacent facets share two common vertices across an edge.
• Highly curved surfaces must be meshed with small faces to eliminate large changes in surface slope between neighboring facets.

Since 2019 R2, Curvilinear Meshing in SBR+ is supported for a) curved-surface geometries built within HFSS and b) imported geometries that retain explicit surface curvature information, such as SAT and IGES format models. With curvilinear meshing, accurate curvature information from the objects is directly used by the SBR+ solver. With curvature extraction, an algorithm is deployed to recover or infer information that was either lost at some point prior to synthesis and import of the faceted model, or that was never available to begin with, so it is necessarily an approximation. Curvilinear meshing is therefore preferred over curvature extraction in those situations where it is available for use with SBR+.

Since 2019 R2, explicitly flat surfaces can be specified to the SBR+ solution by selecting Disable Curvature Extraction for Faceted Surfaces. Users may disable curvature extraction for specific flat surfaces and introduce polygonal surfaces with flat curvatures. When SBR rays reflect off explicitly flat surfaces, the divergence/convergence rate of their associated ray-tube is not modified as it would be with a curved reflecting surface. Also, the creeping wave rays will not propagate over explicitly flat surfaces, as the creeping wave formulation assumes surfaces have finite (non-zero) convex curvature.

Ray-tube Divergence Correction

In SBR+, the one-dimensional rays traced on the CAD model actually represent volumetric ray tubes whose cross-sections are precisely maintained through multiple reflections and transmissions. The 1-D rays shown in the visual ray tracer reside in the centers of these ray tubes.

When rays are launched from a point and represent a spherical wavefront, as with rays launched from antenna sources, their cross-sectional area grows in proportion to R², where R is the propagation distance. Correspondingly, GO fields of the ray tubes decrease as 1/R. This is known as ray-tube divergence. When a ray (tube) reflects off of a flat surface, the rate of ray-tube divergence is unchanged, where R is taken as the total path distance of the ray when starting from the Tx antenna.

Reflection off a curved surface is more complicated. When a ray tube reflects off a convex surface, its rate of divergence increases. When reflecting off a concave surface, its rate of divergence decreases. If the surface has enough concavity, the ray tube will actually start to converge and pass through one or two caustics (focus points) before diverging again. In this process, the shape of the ray tube changes as it propagates. With CAD models described by curved surfaces, SBR+ accounts for this effect precisely, considering both the non-spherical curvature of the incident wavefront (if the ray already reflected off another curved surface) and also localized curvature conditions of the CAD model at the ray hit point. It is important to capture this effect, as it influences the distribution and strength of currents painted on surfaces after the reflection, and these are the currents that determine the scattered field.

In the case of an incident plane-wave source, as when using SBR+ to compute RCS, a set of rays is launched in parallel toward the scattering geometry. In consequence, the associated ray-tubes initially have zero rate of divergence, and this condition will be preserved after the rays reflect off flat surfaces. However, upon encountering curved surfaces of the scattering geometry, the reflecting ray tubes will start to converge or diverge, depending on details of the surface curvature and the angle of incidence relative to the surface perpendicular at the ray hit point.

Dynamic meshing, Tolerant Meshing, Lightweight geometry

Unlike FEM or IE, the ray-tracing methodology of SBR+ does not require sub-wavelength meshing of the scattering geometry. Rather, it is sufficient that the mesh accurately represents the shape of the scattering geometry. For large CAD models when interactive 3D visualization manipulations, geometry meshing, or post-meshing SBR+ simulation becomes too time consuming, one may consider using the relaxed import and meshing options described below.

Note that all of these relaxed meshing options skip the automated process of identifying and eliminating overlapping (coplanar) surfaces. When overlapping surfaces are passed to the SBR+ solver, this can confuse its ray-tracing engine, leading to unexpected and inaccurate results. For example, coplanar surfaces create ambiguity as to which surface was actually hit first, and this can lead to trapped rays bouncing between them. Therefore, when using these relaxed import/meshing options, there is greater responsibility upon the user to avoid the introduction of overlapping surfaces.

Lightweight geometry

Importing large STL files into Ansys Electronics Desktop can be time consuming. STL files contain triangle surface meshes. Importing them to the modeler creates one face entity for each STL triangle and one edge entity for each triangle edge. This can result in a large number of faces and edges, leading to sluggish interactive behavior with 3D visualization. The lightweight geometry import option for STL models bypasses this overhead and associated meshing operations, passing the original STL mesh directly to the SBR+ simulation engine. This results in more responsive UI operations and faster SBR+ simulations.

Dynamic meshing

Dynamic Meshing eliminates mesh generation during SBR+ simulations, which can significantly reduce simulation time. When importing STL models with the Lightweight Geometry option, Dynamic Meshing is automatically engaged (and it cannot be switched off). However, even when Lightweight Geometry has not been engaged, Dynamic Meshing can be switched on in the Initial Mesh Settings dialog in order to receive the benefits of bypassing potentially expensive meshing operations prior to engaging the SBR+ solver.

Tolerant Meshing

If the design contains an SBR+ Region, the Initial Mesh Settings window will include a Tolerant Meshing option. This is because the SBR+ ray-tracing solver has relaxed surface meshing requirements relative to other HFSS solvers. If an imported scattering geometry for the SBR+ region contains anomalies that make it too time-consuming or impossible to use Auto (default) meshing, the tolerant meshing option should be attempted, as it will often result in a successful meshing of the geometry in cases where Auto does not. On the other hand, if the imported geometry is clean and Auto meshing works well, Tolerant Meshing can sometimes result in an excessive number of surface mesh triangles that increase SBR+ solution time. The best meshing option for SBR+ is very dependent on the quality of the imported geometry, so users need to consider both approaches and choose the one that works best for their particular scattering geometry.