Article on a new open source structured mesh generator

Article on a new open source structured mesh generator for electromagnetic simulation tools accepted for publication in IEEE Antennas and Propagation Magazine.

This article provides an overview of the AEG mesh generator, an open source structured mesh generator for creating uniform and non-uniform cuboid meshes. It was primarily developed for generating meshes for finite-difference time-domain (FDTD) and similar electromagnetic solvers.

The example above uses an unstructured STL mesh of a Saab Viggen jet fighter that is available from 3dvia. The unstructured mesh has been mapped onto a cubic structures mesh using the new mesher. The software is script-driven using the MATLAB/GNU Octave language which allows it to be easily extended and combined with other phases of an overall simulation work-flow.

The mesher originated as the project of Erasmus Programme student Mr Michael Berens from the Leibnitz Universität Hannover during his internship at the University of York in 2013. I have since worked on turning the prototype code into a more user focussed modular software package with a test-suite, user documentation and tutorial. I have also added a bounding volume hierarchy (BVH) to improve the efficiency of the mapping stage of the mesh generation.

Full details of the work can be found in the paper (Berens, Flintoft and Dawson, 2016) and the AEG Mesher website.

References

1. Berens, M.K., Flintoft, I.D. and Dawson, J.F., 2016. Structured mesh generation: Open-source automatic nonuniform mesh generation for FDTD simulation. IEEE Antennas and Propagation Magazine, 58(3), pp.45–55.
   

   The finite-difference time-domain (FDTD) method is a numerical technique that is widely used to solve Maxwell’s differential equations in the time domain [1]. Both space and time are discretized. Space is discretized into rectangular-shaped elements in two-dimensional (2-D) or cuboid elements in three-dimensional (3-D). Cuboid elements, where the electric fields are located on the edges of the cuboid and the magnetic fields are normal to the faces, are called Yee cells and are the fundamental elements of most FDTD methods [2]. By filling up the problem space with these cells, we obtain a 3-D mesh, where neighboring cells share edges and faces. Each cell has three associated electric and magnetic field components, while the other field components belong to adjacent cells. The properties of each cell are adjusted to represent materials such as dielectrics or conductors by adjusting the constitutive parameters used in the field equations in the corresponding cells, hence forming the geometrical structure of the problem to be solved. For example, Figure 1 shows a sphere and a version of the sphere discretized using cubic elements.

   @article{Berens2016,
     author = {Berens, M. K. and Flintoft, I. D. and Dawson, J. F.},
     title = {Structured mesh generation: Open-source automatic nonuniform mesh generation for FDTD simulation},
     journal = {IEEE Antennas and Propagation Magazine},
     year = {2016},
     volume = {58},
     number = {3},
     pages = {45-55},
     month = jun,
     issn = {1045-9243},
     note = {Date of acceptance: 08/02/2016. © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.},
     doi = {10.1109/MAP.2016.2541606},
     file = {:pdfs/APM58-Berens-45.pdf:PDF},
     keywords = {Design automation;Finite difference methods;Geometry;Mesh generation;Numerical models;Solid modeling;Time-domain analysis},
     postprint = {https://pure.york.ac.uk/portal/files/46384800/JournalAPM_postprint.pdf},
     publisher = {IEEE}
   }