3 papers
math.NA2025
Implementation and Basis Construction for Smooth Finite Element Spaces
Chunyu Chen, Long Chen, Tingyi Gao +2
The construction of conforming finite elements on simplicial meshes has recently advanced through the groundbreaking work of Hu, Lin, and Wu (Found. Comput. Math. 24, 2024).…
math.AP2025
SOPTX: A High-Performance Multi-Backend Framework for Topology Optimization
Liang He, Huayi Wei, Tian Tian
In recent years, topology optimization (TO) has gained widespread attention as a powerful structural design method. However, its application remains challenging due to the deep exp…
math.NA2025
High-Order Interior Penalty Finite Element Methods for Fourth-Order Phase-Field Models in Fracture Analysis
Tian Tian, Chen Chunyu, Wei Huayi
This paper presents a novel approach for solving fourth-order phase-field models in brittle fracture mechanics using the Interior Penalty Finite Element Method (IP-FEM). The fourth…