Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Generating Sizing Fields for Mesh Generation via GCN-based Simplification of Adaptive Background Grids

Xunyang Zhu, Hongfei Ye, Yifei Wang, Taoran Liu, Jianjun Chen

TL;DR

The paper tackles the challenge of generating a geometry-conforming, computationally lightweight background grid for sizing-field control in unstructured mesh generation. It reframes grid simplification as an edge-classification problem and substitutes costly procedural evaluations with a Graph Convolutional Network that predicts edge scores in a single forward pass. The ABGS framework demonstrates large reductions in background-grid elements (74-94%) and significant query-time savings (35-88%) on complex engineering models, while maintaining geometric fidelity. The work delivers strong practical impact for efficient mesh generation across domains like CFD and electromagnetics and provides public data and code to foster further research.

Abstract

The sizing field defined on a triangular background grid is pivotal for controlling the quality and efficiency of unstructured mesh generation. However, creating an optimal background grid that is geometrically conforming, computationally lightweight, and free from artifacts like banding is a significant challenge. This paper introduces a novel, adaptive background grid simplification (ABGS) framework based on a Graph Convolutional Network (GCN). We reformulate the grid simplification task as an edge score regression problem and train a GCN model to efficiently predict optimal edge collapse candidates. The model is guided by a custom loss function that holistically considers both geometric fidelity and sizing field accuracy. This data-driven approach replaces a costly procedural evaluation, accelerating the simplification process. Experimental results demonstrate the effectiveness of our framework across diverse and complex engineering models. Compared to the initial dense grids, our simplified background grids achieve an element reduction of 74%-94%, leading to a 35%-88% decrease in sizing field query times.

Generating Sizing Fields for Mesh Generation via GCN-based Simplification of Adaptive Background Grids

TL;DR

The paper tackles the challenge of generating a geometry-conforming, computationally lightweight background grid for sizing-field control in unstructured mesh generation. It reframes grid simplification as an edge-classification problem and substitutes costly procedural evaluations with a Graph Convolutional Network that predicts edge scores in a single forward pass. The ABGS framework demonstrates large reductions in background-grid elements (74-94%) and significant query-time savings (35-88%) on complex engineering models, while maintaining geometric fidelity. The work delivers strong practical impact for efficient mesh generation across domains like CFD and electromagnetics and provides public data and code to foster further research.

Abstract

The sizing field defined on a triangular background grid is pivotal for controlling the quality and efficiency of unstructured mesh generation. However, creating an optimal background grid that is geometrically conforming, computationally lightweight, and free from artifacts like banding is a significant challenge. This paper introduces a novel, adaptive background grid simplification (ABGS) framework based on a Graph Convolutional Network (GCN). We reformulate the grid simplification task as an edge score regression problem and train a GCN model to efficiently predict optimal edge collapse candidates. The model is guided by a custom loss function that holistically considers both geometric fidelity and sizing field accuracy. This data-driven approach replaces a costly procedural evaluation, accelerating the simplification process. Experimental results demonstrate the effectiveness of our framework across diverse and complex engineering models. Compared to the initial dense grids, our simplified background grids achieve an element reduction of 74%-94%, leading to a 35%-88% decrease in sizing field query times.

Paper Structure

This paper contains 23 sections, 2 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Definition of 3D Manifold Sizing Field and Background Grid
  3. Methodology
  4. Procedural Framework for Adaptive Simplification
  5. Size Field Initialization
  6. Pre-edge Ranking
  7. Accurate Edge Estimation
  8. Size Field Post-processing
  9. GCN-Accelerated Framework for Adaptive Simplification
  10. Application of GCN
  11. Feature Vector
  12. Node Features
  13. Edge Features
  14. Model Architecture
  15. Branch 1: Node Feature Branch (Global Context Path)
  16. ...and 8 more sections

Figures (8)

  • Figure 1: Several common issues with background grids.
  • Figure 2: Schematic illustration of the adaptive background grid generation process.
  • Figure 3: The workflow of the procedural adaptive background grid coarsening framework.
  • Figure 4: The gradient of the sizing field.
  • Figure 5: The workflow of the GCN-based adaptive background grid coarsening framework.
  • ...and 3 more figures