Fast dynamical simulation combining harmonic-modal hybrid formulations with space separated representations

In our previous works, we addressed degenerated 3D domains by proposing the use of Proper Generalized Decomposition (PGD)-based separated representations, enabling efficient and accurate resolutions in complex geometries. Separately, we also developed a harmonic-modal analysis approach that combined modal and harmonic ingredients to efficiently perform time-integration of nonlinear soil behavior. This was achieved through the offline construction of a parametric dynamic response solution using PGD-based model order reduction techniques. Building upon these advancements, this paper extends the use of harmonic-modal hybrid formulations to dynamical problems in degenerated domains. The integration of space-separated representations allows for extremely fine 3D resolutions while maintaining computational complexity at a significantly reduced order of magnitude. The primary contribution of this work lies in coupling harmonic-modal analysis with space-separated representations, combining the strengths of these methods. The performance and versatility of the proposed approach are demonstrated through the resolution of three illustrative problems: a 3D thermal analysis of a thin plate, a laminated plate, and a 3D elastodynamic analysis of a plate. These examples highlight the method's capability to handle high-resolution 3D problems efficiently, reducing it to a sequence of 1D or 2D problems, enabling significant computational time savings compared to the Finite Element Method (FEM). •Extension of harmonic-modal hybrid formulations to degenerated domains.•PGD-based space-separated representations enabling fine 3D resolutions with low complexity.•Demonstrated on 3D thermal problems of thin and laminated plates.•Application to 3D elastodynamic plate problems in structural dynamics.•Efficient computational performance in high-resolution simulations.