Abstract

Mesh generation, as one of six basic research directions identified in NASA Vision 2030, is an important area in computational geometry and plays a fundamental role in numerical simulations in the area of finite element analysis (FEA) and computational fluid dynamics (CFD). With the rapid progress of high-performance computing hardware, mesh generation methods are required to handle geometric domains with more complex shapes and higher resolution in reliable and fast fashions. Yet, existing mesh generation methods suffer from high computational complexity, low mesh quality in complex geometries, and speed limitations, and have continued to be the bottleneck in those simulation tasks.

This thesis addresses the quadrilateral mesh generation problem from three aspects, element extraction, sequential decision making, and data generation, and their combinations. First, a self-learning system, FreeMesh-S, for finite element extraction system is investigated. Element extraction is a major mesh generation method for its capabilities to generate high-quality meshes around the domain boundary and can be formulated into a sequential decision making process. Three kinds of primitive element extraction rules are conceptually identified. FreeMesh-S, then learns the rules by 1) sampling the element generation rules by a reinforcement learning (RL) algorithm, 2) extracting high quality samples, and 3) training the final rules by a feedforward neural network (FNN). The comprehensive experiments demonstrate the effectiveness of the self-learned meshing rules by FreeMesh-S.

Second, an RL-based computational framework for automatic mesh generation is proposed to improve algorithm automation further. A state-of-the-art RL algorithm, soft actor-critic (SAC), is used to learn the mesh generator's policy from trials. It achieves a fully automatic mesh generation without human intervention and any extra clean-up operations, which are typically needed in current commercial software. The reward function is carefully designed to balance the contradiction between the instant element quality and the remaining boundary quality, in order to achieve an overall high quality mesh. The experiments have shown the competitive performance with two representative meshing methods with respect to generalizability, robustness, and effectiveness. The potentials of mesh generation as a benchmark problem for RL are also identified.

Last, a quality function-based data generation method for the meshing algorithm is devised to increase learning efficiency and algorithm performance. For any data-driven algorithms, high quality and balanced data are essential and deterministic to the performance. This method samples the input-output of the three rules according to their feature spaces; selects high quality samples by a quality function that evaluates if the output is an appropriate solution to the input; and trains an FNN model to simulate the mapping relation via the obtained data. The experiments show that the learning time is greatly reduced while the model has competitive performance comparing with other meshing methods.

To conclude, this thesis combines artificial intelligence techniques, rule-based system, neural networks, and RL, to automate the quadrilateral mesh generation while significantly reducing the time and expertise needed during the creation of high quality mesh generation algorithm. All the techniques can be directly generalized to 3D mesh generation.