We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach extends the strategy proposed in [1] to the numerical resolution of the linear elasticity problem on a computational domain that is more general than a square. The resulting method [2] substantially decreases memory usage and achieves a notable reduction in rank compared to other established Finite Element implementations. This performance gain, however, requires a fundamental rethinking of how core finite element operations are implemented, which includes changes to mesh discretization, node, and degree of freedom ordering, stiffness matrix, and internal nodal force assembly, and the execution of algebraic matrix-vector operations. In this talk, we discuss these aspects in detail and show the method’s performance in the numerical approximation of representative test cases.
A Low-Rank QTT-based Finite Element Method For Elasticity Problems
Elena Benvenuti
;
2026
Abstract
We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach extends the strategy proposed in [1] to the numerical resolution of the linear elasticity problem on a computational domain that is more general than a square. The resulting method [2] substantially decreases memory usage and achieves a notable reduction in rank compared to other established Finite Element implementations. This performance gain, however, requires a fundamental rethinking of how core finite element operations are implemented, which includes changes to mesh discretization, node, and degree of freedom ordering, stiffness matrix, and internal nodal force assembly, and the execution of algebraic matrix-vector operations. In this talk, we discuss these aspects in detail and show the method’s performance in the numerical approximation of representative test cases.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
