We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based on the Hamiltonian formalism. The novelty of this work lies in the implementation of a solver that is halfway between Modal Decomposition and the conventional PGD framework, so as to accelerate the fixed-point iteration algorithm. Additional procedures such that Aitken's delta-squared process and mode-orthogonalization are incorporated to ensure convergence and stability of the algorithm. Numerical results regarding the ROM accuracy, time complexity, and scalability are provided to demonstrate the performance of the new solver when applied to dynamic simulation of a three-dimensional structure.

翻译：本文提出了一种适用于线性弹性动力学问题降阶建模的Proper Generalized Decomposition（PGD）求解器。该求解器主要致力于提升基于哈密顿形式体系的前期PGD求解器的计算效率。本文的创新之处在于实现了一种介于模态分解与传统PGD框架之间的求解器，以加速不动点迭代算法。此外，还融入了Aitken δ²过程和模态正交化等额外步骤，以确保算法的收敛性与稳定性。文中提供了关于降阶模型精度、时间复杂度和可扩展性的数值结果，以展示该新求解器在三维结构动态仿真中的应用性能。