Three-dimensional automatic mesh generation for hybrid electromagnetic simulations

Hybrid mesh generation is required for finite-difference time-domain/finite-element time-domain (FDTD/FETD) hybrid simulations. A combined approach is presented to automatically generate Cartesian/tetrahedral hybrid meshes for open and closed structures. This approach first generates a buffer zone that surrounds a target with specified tightness. The advancing-front technique with ldquosweep-and-retryrdquo is subsequently applied to generate an initial tetrahedral mesh that fills the buffer zone. Finally, the tetrahedral mesh undergoes a combined quality improvement procedure. Due to the low profile of the resulting tetrahedral mesh, the sparse Cholesky decomposition can be applied effectively to solve the resulting FETD matrix. Several examples are provided to demonstrate the main features and the performance of the proposed automatic mesh-generation method.

[1]  Carl Ollivier-Gooch,et al.  A Cost/Benefit Analysis of Simplicial Mesh Improvement Techniques as Measured by Solution Efficiency , 2000, Int. J. Comput. Geom. Appl..

[2]  Paul-Louis George,et al.  Back to Edge Flips in 3 Dimensions , 2003, IMR.

[3]  Matthew L. Staten,et al.  An Approach to Combined Laplacian and Optimization-Based Smoothing for Triangular, Quadrilateral, and Quad-Dominant Meshes , 1998, IMR.

[4]  Dongsoo Koh,et al.  A hybrid full-wave analysis of via hole grounds using finite difference and finite element time domain methods , 1997, IMS 1997.

[5]  S. Canann,et al.  Optismoothing: an optimization-driven approach to mesh smoothing , 1993 .

[6]  R. J. Joseph,et al.  Advances in Computational Electrodynamics: The Finite - Di erence Time - Domain Method , 1998 .

[7]  P. L. George,et al.  Automatic Mesh Generation: Application to Finite Element Methods , 1992 .

[8]  Lori A. Freitag,et al.  On combining Laplacian and optimization-based mesh smoothing techniques , 1997 .

[9]  D. A. Field.  Laplacian smoothing and Delaunay triangulations , 1988 .

[10]  Jin-Fa Lee,et al.  Automatic mesh generation using a modified Delaunay tessellation , 1997 .

[11]  Roger I. Tanner,et al.  Generation of unstructured tetrahedral meshes by advancing front technique , 1993 .

[12]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[13]  Paresh Parikh,et al.  Generation of three-dimensional unstructured grids by the advancing-front method , 1988 .

[14]  A. C. Woo,et al.  Benchmark radar targets for the validation of computational electromagnetics programs , 1993 .

[15]  Bharat K. Soni,et al.  Mesh Generation , 2020, Handbook of Computational Geometry.

[16]  Paresh Parikh,et al.  Generation of three-dimensional unstructured grids by the advancing-front method , 1988 .

[17]  J. Schenck,et al.  An efficient, highly homogeneous radiofrequency coil for whole-body NMR imaging at 1.5 T , 1985 .

[18]  Robert J. Lee,et al.  Improved-accuracy algorithms for time-domain finite methods in electromagnetics , 2003 .

[19]  Thomas Rylander,et al.  Stable FEM-FDTD hybrid method for Maxwell's equations , 2000 .

[20]  R. Mittra,et al.  Time-domain (FE/FDTD) technique for solving complex electromagnetic problems , 1998 .

[21]  Jin-Fa Lee,et al.  Time-domain finite-element methods , 1997 .

[22]  Woo-Young Choi,et al.  Tetrahedral mesh generation based on advancing front technique and optimization scheme , 2003 .

[23]  Bharat K. Soni,et al.  Handbook of Grid Generation , 1998 .

[24]  Carl Ollivier-Gooch,et al.  Tetrahedral mesh improvement using swapping and smoothing , 1997 .

[25]  Kenji Shimada,et al.  An Angle-Based Approach to Two-Dimensional Mesh Smoothing , 2000, IMR.

[26]  J. Bonet,et al.  An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problems , 1991 .

[27]  J.-L. Coulomb,et al.  A pyramidal element to link hexahedral, prismatic and tetrahedral edge finite elements , 1997 .

[28]  L. Freitag,et al.  Tetrahedral mesh improvement via optimization of the element condition number , 2002 .

[29]  A. Rassineux,et al.  GENERATION AND OPTIMIZATION OF TETRAHEDRAL MESHES BY ADVANCING FRONT TECHNIQUE , 1998 .

[30]  R. Mittra,et al.  A new stable hybrid three-dimensional generalized finite difference time domain algorithm for analyzing complex structures , 2005 .

[31]  R. B. Simpson,et al.  A framework for advancing front techniques of finite element mesh generation , 1995 .