You are here

Automatic Hexahedral Mesh Generator for the Electromagnetic Modeling of Complex Navy Platforms with Array Antennas and Radomes






OBJECTIVE: Develop an advanced tool for automatically generating hexahedral meshes for high-fidelity simulation of electronically scanned array antennas on Navy platforms.


DESCRIPTION: Currently, many powerful fully automatic mesh generation tools are available that employ tetrahedral cells to mesh complex geometries, including full aircraft Computer-aided Design (CAD) models. These tetrahedral meshes are in general unable to provide the same level of solution accuracy as hexahedral meshes. Another important advantage of a hexahedral mesh over a tetrahedral mesh is the reduction in the number of elements for the same level of analysis accuracy. However, creating hexahedral meshes, especially for complex geometries such as full aircraft, is a tedious and time-consuming process that significantly burdens many realistic engineering analyses and design cycles.


Conducting performance analysis of very complex antennas on full aircraft configuration for Navy applications can be significantly improved by employing a hexahedral mesh. Such antennas include passive phased array (PESA), active electronically scanned array (AESA), hybrid beam forming phased array, and digital beam forming (DBF) array. These types of antennas have small-scale complex internal features that need to be precisely captured by a given mesh. At the same time, the location of these antennas on the aircraft is also important and needs to be optimized. As such, the combination of greatly varying mesh scales and the number simulations that need to be performed are significant factors that can take advantage of a hexahedral mesh that will allow for better accuracy with significantly reduced overall simulation time. The ability to produce highly accurate on-aircraft antenna responses at the element level (fractions of a dB in the main beam) while reducing run-time by adaptively meshing the model is critical. Taking advantage of the latest developments in hexahedral meshing technology [Refs 1–3] to create fully hexahedral or strongly hex-dominant (98% or more hex) meshes for applications involving installed phased array antennas on full aircraft configurations is a possible means to address this topic. The approach should provide capabilities to import CAD models (IGES, STEP, STL, etc.) and subsequent geometry cleanup and preparation for meshing. Provide capabilities to write out mesh in CGNS format for subsequent use with EM simulation tools.


PHASE I: Demonstrate the feasibility of an automatic hexahedral mesh, or a hexahedral dominant mesh generation tool, for simulation of complex phased array antennas on full aircraft platforms. Initiate development work on a user friendly Graphic User Interface (GUI) or integrate into an existing mesh generation tool to enable the user to efficiently (relative to that of existing commercial codes using tetrahedral meshing), set up a geometry model and create a hexahedral mesh capturing details of the antenna and aircraft geometry. The demonstration should compare accuracy of simulations using the hexahedral meshes with those using tetrahedral meshes for a variety of canonical electromagnetic problems.. The Phase I effort will include prototype plans to be developed under Phase II.


PHASE II: Develop a prototype hexahedral mesh generator tool. Continue work on further development and improvement of the algorithm initiated during Phase I. Complete the related GUI development work. Include performance metrics using advanced EM simulation tools to show expected performance efficiencies compared to conventional tetrahedral meshes. Show ease of use and operability utilizing realistic CAD models of installed phased array antennas on the aircraft. Provide the option of creating tetrahedral meshes as needed by the end user.


PHASE III DUAL USE APPLICATIONS: Complete development, and perform final testing of a commercial grade application for use by radar, antenna, and computational electromagnetics engineers.


The approach is applicable to any electrically large complex system including commercial aircraft or automobiles.



  1. Livesu, M., Pietroni, N., Puppo, E., Sheffer, A., & Cignoni, P. (2020). “LoopyCuts: practical feature-preserving block decomposition for strongly hex-dominant meshing.” ACM Transactions on Graphics (TOG), 39(4), 121-1.
  2. Li, Y., Liu, Y., Xu, W., Wang, W., & Guo, B. (2012). “All-hex meshing using singularity-restricted field.” ACM Transactions on Graphics (TOG), 31(6), 1-11.
  3. Liu, H., Zhang, P., Chien, E., Solomon, J., & Bommes, D. (2018). “Singularity-constrained octahedral fields for hexahedral meshing.” ACM Transactions on Graphics, 37(4), Article No. 93, 1.


KEYWORDS: computational electromagnetics; Hexahedral Mesh; modeling and simulation; antennas; radome; antenna array

US Flag An Official Website of the United States Government