Lei Zhang

Mingjie Liao, Ping Lin, Lei Zhang

In this paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum (a/c) coupling with finite range interactions in two dimensions. We have systematically derived a new explicitly computable stress tensor formula for finite range interactions. In particular, we use the geometric reconstruction based consistent atomistic/continuum (GRAC) coupling scheme, which is optimal if the continuum model is discretized by $P^1$ finite elements. The numerical results of the adaptive mesh refinement algorithm is consistent with the optimal a priori error estimates.

Zetao Ma, Jingrun Chen, Rui Du et al.

In this work, we develop a numerical homogenization approach for the fully nonlinear Landau-Lifshitz equation with rough coefficients, including non-periodicity and nonseparable scales. Direct numerical resolution of such multiscale problems on fine meshes incurs prohibitive computational costs. To address this challenge, we propose an efficient coarse scale approximation through localized basis functions derived from energy minimization within the Generalized Rough Polyharmonic Splines (GRPS) framework. These basis functions preserve critical multiscale features while operating on a computationally tractable coarse mesh. The nonlinear, vectorial, and non-symmetric nature of the Landau-Lifshitz equation necessitates careful design of variational formulations for basis construction. We introduce several such formulations, each tailored to specific structural aspects of the problem. Through systematic numerical experiments, we demonstrate that our approach achieves significant computational savings without compromising accuracy, offering a robust framework for simulating multiscale magnetic systems with complex microstructures.

Xi-An Li, Lei Zhang, Li-Yan Wang et al.

Understanding the implication of point cloud is still challenging to achieve the goal of classification or segmentation due to the irregular and sparse structure of point cloud. As we have known, PointNet architecture as a ground-breaking work for point cloud which can learn efficiently shape features directly on unordered 3D point cloud and have achieved favorable performance. However, this model fail to consider the fine-grained semantic information of local structure for point cloud. Afterwards, many valuable works are proposed to enhance the performance of PointNet by means of semantic features of local patch for point cloud. In this paper, a multi-scale receptive fields graph attention network (named after MRFGAT) for point cloud classification is proposed. By focusing on the local fine features of point cloud and applying multi attention modules based on channel affinity, the learned feature map for our network can well capture the abundant features information of point cloud. The proposed MRFGAT architecture is tested on ModelNet10 and ModelNet40 datasets, and results show it achieves state-of-the-art performance in shape classification tasks.