Adaptive Meshing Guidelines for Ansoft HFSS - Tetrahedral Refinement, Frequency Selection

1. Guidelines for Meshing in Ansoft HFSS Ansoft Corporation Four Station Square, Suite 200 Pittsburgh, PA 15219-1119 USA (412) 261-3200

2. Topics Covered • Adaptive Meshing Overview • Description • Choosing Adapt Frequency • Driven Solution Mesh Guidelines • Frequency and Adaptation Criteria • Mesh Settings • Seeding and Manual Refinement • Eigenmode Solution Mesh Considerations • Examples

3. Adaptive Meshing Overview Filter Posts • Adaptive meshing is performed at a single frequency specified by the user • Model behavior is explored systematically by solving gradually denser meshes • Mesh density is added where necessary, not indiscriminately • Solution progress is evaluated after each adaptive mesh is solved based on the convergence criteria • Criterion 1: Number of Passes • Criterion 2: Maximum Delta-S • Maximum Delta-S is the worst-case vector magnitude change of any S-parameter’s solution from Pass N as compared to its solution from Pass (N-1). • Per-Parameter criteria also available • 95% of HFSS Project Setups Should Use at Least Some Adaptation!!! Note how mesh density is greater in the region between filter posts, where wave energy is superposed by reflections

4. Overview: Tetrahedral Refinement • Tetrahedral Refinement is based on percentage of the prior mesh • This maintains a consistent “lever arm” for solution changes • If the mesh grows too quickly, subsequent solutions may be accurate, but take excessive computer resources and time • If the mesh grows too slowly (e.g. a fixed tet growth count, rather than percentage), the “lever arm” shrinks with respect to the problem, and solutions may appear to converge before an accurate solution is reached • The default Tet. Refinement value is 20%. This is adequate for the vast majority of HFSS projects. Convergence data below is shown for a model using the default 20% tetrahedral refinement criterion. Had the number of new tetrahedra been kept level, the solution would likely have exited on or around Pass 5.

5. Choosing Adapt Frequency For this band-pass filter, adapting here will result in mesh refinement inside the filter structure, capturing its behavior... • Proper adaptive frequency selection is very important to solution accuracy • Initial mesh and subsequent adaptation are in part wavelength dependent • Despite convergence, the mesh may be too coarse for good results at higher frequencies with a significantly smaller wavelengths • Adaptive frequency recommendations: • For single-frequency or narrow-band solutions (insignificant change in ): Adapt at frequency of interest • For wide-band solutions: Adapt between the middle and high ends of the band (smaller wavelength) • Caution: If you want to view behavior over a specific band, but the device’s response is more narrow, adapt within the device’s bandwidth ...while adapting here may only permit tetrahedral refinement at the ends of the filter, where the energy is being rejected.

6. Driven Solutions: Mesh Selection • Solutions can begin with several different meshes • For the first solution performed, the initial mesh is generally used • Initial mesh uses lambda refinement by default, and can also utilize seed refinement • If adaptive passes have been solved (at one or more adaptive frequencies) the current or previous mesh can be used • Current allows continuation of the adaptation process if the desired number of passes was reached before the desired delta-S value. • Previous allows the user to take a step back from an overly large mesh • For the first or subsequent solution(s), the user may elect to create a manual mesh • The Mesh Options button allows further definition for either the Initial or the Manual meshes

7. Initial Mesh Options: Seeding • Lambda Refinement is the default initial mesh setting • The mesher will assure that tetrahedral edge lengths are on the order of /4 • The Define Seed Operations button accesses the graphical meshing interface • Here, the user selects objects, object faces, or box subregions within the model to apply mesh seeding • Seeding is application of additional ‘vertices’ with a specified spacing within the model • Seeding is acted upon when the solution process begins meshing the project

8. 1. 2. 3. 4. Initial Mesh Options: Seeding Method • Select an object, face, or combination thereof in which a seeding parameter is desired. • From the Seed menu, select Object to seed the volume, or Object Face to seed surfaces • Box does not require prior object selection; the interface will prompt for the box location in which to apply seeding. • Define whether seeding should be by (tet edge) length, (triangular face) area, or (tetrahedral) volume. • Define seed dimension (in the active drawing’s units) and tetrahedral count restraints

9. Manual Mesh Options • To create a Manual Mesh, first select the mesh to use • Options will be the same as those available for solution, depending on the project’s current status • The Define Manual Mesh button activates the graphical meshing interface • This is the same interface used for mesh seeding. However, in Manual Mesh mode the seeding operations are disabled • The interface is used to directly generate a mesh based on user inputs • Manual meshing options are identical to the seeding options

10. Manual Mesh Options: Procedure 1. • Select an object, object face, or combination thereof • From the Refine menu, pick whether you want to refine the mesh in the object volume or on its faces • Box requires no prior geometry selection • Select whether to refine by length, area, volume, etc. • Provide refinement dimension criteria and mesh growth limit • Continue through all objects to be manually refined • NOTE: Since you are generating a MANUAL mesh, Lambda Refinement will NOT be performed on any objects you neglect! 2. 3. 4.

11. When to Seed or Manual Mesh • Some model types do not solve efficiently using adaptive refinement alone; these options can speed convergence • High Dielectric Constants: Materials with high dielectric constants solve better if seeded or manually meshed due to their smaller effective wavelength • Locally Strong Field Gradients: Some structures, such as the capacitively-loaded cavity on the lower left, have features whose influence on the behavior is not wavelength-driven • Extreme Aspect Ratios: Models with very high aspect ratios are harder to mesh with ‘high quality’ tetrahedra; manual or seed-based assistance can improve the mesh quality and resultant matrix condition Cylindrical Dielectric Resonator in Cavity. Dielectric Puck has r = 90. Wavelength is only 1/10 that in surrounding air volume! Seeded to /4 in the material to compensate. Cavity structure at right has post extending from bottom to almost touch the top. The narrow capacitive gap between the post end face and the cavity end itself has a virtual solid defined to allow manual meshing where fields will be very strong

12. Eigenmode Meshing Options • Eigenmode Solution Starting Mesh selectionand Initial and Manual Mesh Options are identical to those for driven solution • Initial Mesh Options accesses the mesh seeding interface • Manual Mesh Options accesses the graphical mesher for direct user-refined meshing

13. Example 1: Reactive Coupling • Seed coupling structures that are << l • Seed/manually mesh reactive regions

14. Example 2: Lead-Frame Initial mesh for lead-frame that has high aspect ratio objects

15. Example 2: Lead-Frame (detail) • Initial mesh shows long, skinny surface triangles • May need seeding or manual refinement to fully capture field behavior • Note: It is always a good idea to try adaptive solutions to evaluate if user modification of the mesh is required.

16. Example 3: Flat Panel LCD

17. Example 3: Flat Panel LCD (detail) Many thin objects closely packed and stacked

18. Example 4: Spiral Inductor • 8 turn spiral • 2 micron thick traces • 0.8 micron gap • 200 micron square

19. Example 4: Spiral Inductor • Initial mesh is sparse on traces (in gap region also) • Seeding/Manual meshing may be needed to characterize spiral properly • Due to small electrical size, may need: • Skin Depth meshing • Solve Inside conductors • If electrical size << l • Create large dense mesh • Use ZERO_ORDER_MODE for the solution