Domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) nonlinear model reduction

Abstract

A novel domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) model-reduction method applicable to parameterized systems of nonlinear algebraic equations (e.g., arising from discretizing a parameterized partial-differential-equations problem) is proposed. In contrast with previous works, we adopt an algebraically non-overlapping decomposition strategy rather than a spatial-decomposition strategy, which facilitates application to different spatial-discretization schemes. Rather than constructing a low-dimensional subspace for the entire state space in a monolithic fashion, the methodology constructs separate subspaces for the different subdomains/components characterizing the original model. In the offline stage, the method constructs low-dimensional bases for the interior and interface of components. In the online stage, the approach constructs an LSPG ROM for each component and enforces strong or weak compatibility on the 'ports' connecting them. We propose four different ways to construct reduced bases on the interface/ports of subdomains and several ways to enforce compatibility across connecting ports. We derive a posteriori and a priori error bounds for the DD-LSPG solutions. Numerical results performed on nonlinear benchmark problems in heat transfer and fluid dynamics demonstrate that the proposed method performs well in terms of both accuracy and computational cost, with different choices of basis and compatibility constraints yielding different performance profiles.

43 pages, 17 figures

References in corpus (7)

• A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
• Component-wise reduced order model lattice-type structure design
• Reduced order models for Lagrangian hydrodynamics
• Accelerating design optimization using reduced order models
• Efficient nonlinear manifold reduced order model
• Projection-based model reduction of dynamical systems using space-time subspace and machine learning
• In-situ adaptive reduction of nonlinear multiscale structural dynamics models

Cited by in corpus (21)

• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• LaSDI: Parametric Latent Space Dynamics Identification
• Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques
• Component-wise reduced order model lattice-type structure design
• Parametric Dynamic Mode Decomposition for Reduced Order Modeling
• Reduced order models for Lagrangian hydrodynamics
• gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification
• Efficient space-time reduced order model for linear dynamical systems in Python using less than 120 lines of code
• A fast and accurate domain-decomposition nonlinear manifold reduced order model
• S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models
• Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties
• A one-shot overlapping Schwarz method for component-based model reduction: application to nonlinear elasticity
• Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning
• Projection based semi--implicit partitioned Reduced Basis Method for non parametrized and parametrized Fluid--Structure Interaction problems
• Domain decomposition for data-driven reduced modeling of large-scale systems
• An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition
• A hyperreduced reduced basis element method for reduced-order modeling of component-based nonlinear systems
• Projection-based model reduction of dynamical systems using space-time subspace and machine learning
• Windowed space-time least-squares Petrov-Galerkin method for nonlinear model order reduction
• A reduced order model for domain decompositions with non-conforming interfaces
• A short perspective on a posteriori error control and adaptive discretizations