arXiv subjects

Qingsong Duan

Publications and source records attributed to Qingsong Duan.

2 recordsLinked to original sources

arXiv2025

Three dimensional seepage analysis using a polyhedral scaled boundary finite element method

This work presents a polyhedral scaled boundary finite element method (PSBFEM) for three dimensional seepage analysis. We first derive the scaled boundary formulation for 3D seepage problems, and subsequently incorporate Wachspress shape functions to construct shape functions over arbitrary polygonal elements, thereby establishing the foundation of the proposed polyhedral SBFEM. The method combines the semi-analytical nature of the SBFEM with the geometric flexibility of polyhedral and octree meshes, making it well-suited for complex seepage simulations. The PSBFEM is implemented within the ABAQUS UEL framework to facilitate steady-state, transient, and free-surface seepage analyses. A series of numerical examples are conducted to verify the accuracy, efficiency, and convergence properties of the proposed approach, including benchmark tests and applications with intricate geometries. The results demonstrate that the PSBFEM achieves higher accuracy and faster convergence than conventional FEM, particularly when using hybrid octree meshes with local refinement. This framework provides a robust and efficient computational tool for three-dimensional seepage analysis in geotechnical and hydraulic engineering applications.

math.NA↗

arXiv2025

A polyhedral scaled boundary finite element method solving three-dimensional heat conduction problems

In this study, we derived a three-dimensional scaled boundary finite element formulation for heat conduction problems. By incorporating Wachspress shape functions, a polyhedral scaled boundary finite element method (PSBFEM) was proposed to address heat conduction challenges in complex geometries. To address the complexity of traditional methods, this work introduced polygonal discretization techniques that simplified the topological structure of the polyhedral mesh and effectively integrated polyhedral and octree meshes, thereby reducing the number of element faces and enhancing mesh efficiency to accommodate intricate shapes. The developed formulation supported both steady-state and transient heat conduction analyses and was implemented in ABAQUS through a user-defined element (UEL). Through a series of numerical examples, the accuracy and convergence of the proposed method were validated. The results indicated that the PSBFEM consistently achieved higher accuracy than the FEM as the mesh was refined. The polyhedral elements offered a computationally efficient solution for complex simulations, significantly reducing computational costs.Additionally, by utilizing the octree mesh parent element acceleration technique, the computational efficiency of PSBFEM surpassed that of the FEM.

math.NA↗