Gengdong Cheng

Qingyuan Hu, Franz Chouly, Ping Hu et al.

A simple skew-symmetric Nitsche's formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions, symmetry conditions for Kirchhoff plates, patch coupling in statics and in modal analysis as well as Signorini contact conditions. For linear boundary or interface conditions, the skew-symmetric formulation is parameter-free. For contact conditions, it remains stable and accurate for a wide range of the stabilization parameter. Several numerical tests are performed to illustrate its accuracy, stability and convergence performance. We investigate particularly the effects introduced by Nitsche's coupling, including the convergence performance and condition numbers in statics as well as the extra "outlier" frequencies and corresponding eigenmodes in structural dynamics. We present the Hertz test, the block test, and a 3D self-contact example showing that the skew-symmetric Nitsche's formulation is a suitable approach to simulate contact problems in IGA.

Jie Pan, Jingwei Huang, Gengdong Cheng et al.

This paper proposes, implements, and evaluates a reinforcement learning (RL)-based computational framework for automatic mesh generation. Mesh generation plays a fundamental role in numerical simulations in the area of computer aided design and engineering (CAD/E). It is identified as one of the critical issues in the NASA CFD Vision 2030 Study. Existing mesh generation methods suffer from high computational complexity, low mesh quality in complex geometries, and speed limitations. These methods and tools, including commercial software packages, are typically semiautomatic and they need inputs or help from human experts. By formulating the mesh generation as a Markov decision process (MDP) problem, we are able to use a state-of-the-art reinforcement learning (RL) algorithm called "soft actor-critic" to automatically learn from trials the policy of actions for mesh generation. The implementation of this RL algorithm for mesh generation allows us to build a fully automatic mesh generation system without human intervention and any extra clean-up operations, which fills the gap in the existing mesh generation tools. In the experiments to compare with two representative commercial software packages, our system demonstrates promising performance with respect to scalability, generalizability, and effectiveness.