An efficient PGD solver for structural dynamics applications.

Area of Science:

• Computational Mechanics
• Numerical Analysis
• Solid Mechanics

Background:

• Reduced-order modeling (ROM) is crucial for efficient simulation of complex systems.
• Existing Proper Generalized Decomposition (PGD) solvers for elastodynamics can be computationally intensive.
• Hamiltonian formalism has been previously used for PGD-based ROM.

Purpose of the Study:

• To develop a more computationally efficient PGD solver for linear elastodynamic problems.
• To enhance the performance of existing PGD solvers by accelerating the fixed-point iteration.
• To demonstrate the accuracy, efficiency, and scalability of the proposed solver.

Main Methods:

• Implementation of a hybrid solver combining Proper Generalized Decomposition (PGD) and Modal Decomposition.
• Incorporation of Aitken's delta-squared process for accelerated convergence.
• Application of mode-orthogonalization techniques to ensure algorithmic stability.
• Validation through dynamic simulation of a three-dimensional structure.

Main Results:

• The proposed solver significantly accelerates the fixed-point iteration algorithm.
• Numerical results demonstrate high accuracy in reduced-order modeling (ROM).
• The solver exhibits improved time complexity and scalability compared to conventional methods.

Conclusions:

• The novel PGD solver offers enhanced computational efficiency for linear elastodynamics.
• The hybrid approach effectively balances accuracy and speed for dynamic simulations.
• This method provides a robust and scalable solution for analyzing 3D structures.