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Adaptive mesh refinement for electromagnetic simulation

Alexey Belokrys-Fedotov, Vladimir Garanzha, Lennard Kamenski, Alexandr Chikitkin, Evgeniy Pesnya, Nikita Aseev, Andrey Vorobyev

TL;DR

The paper addresses the challenge of obtaining accurate electromagnetic FEM simulations for complex devices within practical compute budgets by developing a complete adaptive meshing workflow. It combines constrained Delaunay tetrahedralization, Ruppert-type refinement augmented with an anisotropic encroachment domain (AED) to handle thin material layers, robust pre- and post-processing for sliver elimination, and goal-oriented RHS-based error indicators to steer refinement, followed by variational smoothing. The authors introduce the AED strategy, sliver-handling techniques, and a practical AMR pipeline, and validate them against Ansys HFSS on two industrial-like test structures, achieving comparable or better accuracy with smaller meshes and fewer refinement steps. The results demonstrate significant gains in efficiency and robustness for industrial EM simulations, including challenging CAD defects and thin-layer geometries.

Abstract

We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance for the finite element solution of the Maxwell equations, since they directly affect the accuracy and the computational time. In this paper, we describe the complete meshing workflow, which allows the simulation of arbitrary structures. Test simulations confirm that the presented approach allows to reach the quality of the industrial simulation software.

Adaptive mesh refinement for electromagnetic simulation

TL;DR

The paper addresses the challenge of obtaining accurate electromagnetic FEM simulations for complex devices within practical compute budgets by developing a complete adaptive meshing workflow. It combines constrained Delaunay tetrahedralization, Ruppert-type refinement augmented with an anisotropic encroachment domain (AED) to handle thin material layers, robust pre- and post-processing for sliver elimination, and goal-oriented RHS-based error indicators to steer refinement, followed by variational smoothing. The authors introduce the AED strategy, sliver-handling techniques, and a practical AMR pipeline, and validate them against Ansys HFSS on two industrial-like test structures, achieving comparable or better accuracy with smaller meshes and fewer refinement steps. The results demonstrate significant gains in efficiency and robustness for industrial EM simulations, including challenging CAD defects and thin-layer geometries.

Abstract

We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance for the finite element solution of the Maxwell equations, since they directly affect the accuracy and the computational time. In this paper, we describe the complete meshing workflow, which allows the simulation of arbitrary structures. Test simulations confirm that the presented approach allows to reach the quality of the industrial simulation software.
Paper Structure (12 sections, 11 equations, 18 figures, 3 tables, 2 algorithms)

This paper contains 12 sections, 11 equations, 18 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Test Structures
  3. Governing Equations and Electromagnetic Simulation Cases
  4. Finite Element Method and a Posteriori Error Estimates
  5. Tetrahedral Meshing for Models with Thin Material Layers
  6. Structure of the Underlying Algorithms
  7. New Anisotropic Encroachment Domain (AED) Mesh Vertex Insertion Strategy to Account for Thin Material Layers
  8. Pre-processing and Post-Optimization for Sliver Elimination
  9. Testing the Anisotropic Encroachment Domain (AED) Based Algorithm
  10. Adaptive Mesh Refinement (AMR)
  11. Simulation Results
  12. Conclusion

Figures (18)

  • Figure 1: Cavity resonator filter (6cav)
  • Figure 2: Antenna array unit (AAU)
  • Figure 3: Accuracy of error indicators for the AAU with 125k mesh elements. Right: close-in for the fraction from $0$ to $0.05$
  • Figure 4: Ruppert's algorithm simultaneously refines PPLG edges and triangles to meet quality and mesh size requirements while preserving the Delaunay property of the triangulation
  • Figure 5: Anisotropic encroachment domains for boundary edges and faces
  • ...and 13 more figures