Скачать или смотреть [07/11/2025] LaCàN/CIMNE Seminar by Dr Elena Benvenuti

LàCaN/CIMNE Seminar – A low-rank QTT-based finite element method for elasticity problems by Dr Elena Benvenuti

📖 𝗔𝗕𝗦𝗧𝗥𝗔𝗖𝗧

We present an efficient and robust numerical algorithm for solving two-dimensional linear elasticity problems that combines the Quantized Tensor Train format and a domain partitioning strategy. This method substantially decreases memory usage and achieves a notable rank reduction compared to established Finite Element implementations like the FEniCS platform. This performance gain, however, requires a fundamental rethinking of how core finite element operations are implemented, which includes changes to mesh discretization, ordering of nodes and degrees of freedom, stiffness matrix, and internal nodal force assembly, and the execution of algebraic matrix-vector operations. In this work, we discuss all these aspects in detail and assess the method’s performance in the numerical approximation of three representative test cases.


🗣️ 𝗦𝗣𝗘𝗔𝗞𝗘𝗥

Dr. Elena Benvenuti is a Full Professor of Solids and Structural Mechanics at the Engineering Department of the University of Ferrara since 2024 and a Civil Engineering Degree in 1997, PhD in Solids and Structural Mechanics in 2001 at the University of Trent, since 2021 Director of the Civil Engineering Teaching Program, she is expert in computational solid mechanics procedures for solids and structures. Her research activity produced more than 150 scientific papers on international journals and conference proceedings as a single author or in collaboration with international experts. Her publications cover multiple topics, including nonlocal damage, nonlocal elasticity, regularized eXtended Finite Element Method, continuous-discontinuous transition, FRP-delamination, fracture mechanics, nanocomposites, mechanobiology of cell-interface interactions, and, recently, low rank models.