Article
Computer Science, Interdisciplinary Applications
Bastien Bodnar, Walid Larbi, Magdalini Titirla, Jean-Francois Deu, Fabrice Gatuingt, Frederic Ragueneau
Summary: This paper presents a method that combines a hyper-reduction procedure and a non-iterative alpha-OS time-integration scheme for accelerating parametric analyses on damageable civil engineering structures subjected to earthquakes. The method is shown to be applicable and accurate through its application on a specific building model.
COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING
(2023)
Article
Mathematics, Applied
Cecilia Pagliantini, Federico Vismara
Summary: This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields. The method retains the gradient structure and improves computational efficiency. Numerical tests demonstrate faster runtime compared to the full and reduced models.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Mechanical
Nidish Narayanaa Balaji, Tobias Dreher, Malte Krack, Matthew R. W. Brake
Summary: One strategy for developing accurate and computationally feasible models of jointed structures is through reduced order modeling using hyper-reduced representations of contact interfaces. Two fundamentally different approaches, stiffness-preserving constraint elements and interpolation through remeshing, are formulated and compared for their applicability. These approaches are evaluated on a three-bolted lap-joint structure to study characteristic contact non-linearities, with strategies such as graph partitioning and finite element coarsening being assessed for performance.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Computer Science, Interdisciplinary Applications
Sourav Dutta, Matthew W. Farthing, Emma Perracchione, Gaurav Savant, Mario Putti
Summary: This work develops Non-Intrusive Reduced Order Models (NIROMs) that combine Proper Orthogonal Decomposition (POD) with Radial Basis Function (RBF) interpolation method for efficient reduced order models in time-dependent problems. The performance is compared with traditional nonlinear POD (NPOD) model, different greedy algorithms are studied, and a new psr-greedy algorithm is proposed. Experimental results are presented for realistic 2D shallow water flow applications.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Rakesh Halder, Krzysztof J. Fidkowski, Kevin J. Maki
Summary: The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods. However, for some nonlinear problems, linear RB methods are not efficient. Nonlinear manifolds have shown increased performance for certain nonlinear problems over linear methods. In this work, a non-intrusive ROM framework is proposed that uses convolutional autoencoders to provide a nonlinear solution manifold and is augmented by Gaussian process regression (GPR) to approximate the expansion coefficients of the reduced model.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Mechanics
Pin Wu, Feng Qiu, Weibing Feng, Fangxing Fang, Christopher Pain
Summary: This paper proposes a novel method to construct a non-intrusive reduced order model (ROM) using proper orthogonal decomposition and transformer neural network. The method effectively captures flow dynamics and reduces online calculation time. Experimental results demonstrate that the proposed model outperforms other ROMs in capturing flow details and has higher accuracy.
Article
Mechanics
B. Karasozen, S. Yildiz, M. Uzunca
Summary: In this paper, reduced-order models (ROMs) are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with state-dependent Poisson matrix. The ROMs are constructed using proper orthogonal decomposition with Galerkin projection and integrated in time with the average vector field (AVF) method. The computational cost is reduced by approximating the nonlinear terms with the discrete empirical interpolation method. The accuracy and computational efficiency of the ROMs are demonstrated for a numerical test problem.
Article
Engineering, Multidisciplinary
Jack S. Hale, Elisa Schenone, Davide Baroli, Lars A. A. Beex, Stephane P. A. Bordas
Summary: Reduced assembly (RA) is introduced as a new hyper-reduction strategy to drastically reduce the computational costs associated with assembling and projecting large linear systems onto a reduced order basis. RA achieves performance increases up to five times over baseline methods for solving non-linear reaction-diffusion and 3D hyperelasticity problems.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Yongse Kim, Seung-Hoon Kang, Haeseong Cho, Haedong Kim, SangJoon Shin
Summary: This paper presents an improved nonlinear reduced-order modeling technique for describing parameterized shape defects. The proposed framework constructs a reduced-order representation in a polynomial form using a set of pre-determined defect shapes. By employing a quadratic-manifold based approach, the computational expense is greatly reduced while accurately estimating the defect-parametric variation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Murat Uzunca, Buelent Karasoezen
Summary: Reduced-order models (ROMs) are constructed for the Ablowitz-Ladik equation (ALE), an integrable semi-discretization of the nonlinear Schrodinger equation (NLSE) with and without damping. The full-order solutions are obtained using different numerical methods for the conservative and dissipative ALE. The reduced-order solutions are constructed intrusively using proper orthogonal decomposition (POD) with Galerkin projection, and the computation is accelerated by the use of tensor techniques and discrete empirical interpolation method (DEIM).
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Engineering, Mechanical
Ahmed Amr Morsy, Mariella Kast, Paolo Tiso
Summary: The article introduces a method for constructing hyper-reduced order models that accurately simulate the dynamic behavior of jointed assemblies with friction nonlinearities. By using the Multi-Harmonic Balance Method and Galerkin projection, the model order is reduced. The implementation of an adapted Energy Conserving Weighing and Sampling technique allows for significant speedups in evaluating the nonlinear forces. The accuracy and efficiency of the method are demonstrated through two case studies.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Mathematics, Applied
Bulent Karasozen, Suleyman Yildiz, Murat Uzunca
Summary: In this paper, projection-based intrusive and data-driven model order reduction methods are investigated for numerical simulation of rotating thermal shallow water equation. The constructed reduced-order models accurately predict system behavior in both test and training data and achieve significant computational speed-up.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Multidisciplinary Sciences
Rudy Geelen, Karen Willcox
Summary: This paper presents a data-driven approach for learning localized reduced models. By using multiple local approximation subspaces instead of a global reduced basis, the approach allows for adaptation of the reduced model to local dynamics while keeping the reduced dimension small. The contribution of this paper is a non-intrusive method that learns the localized reduced model from snapshot data using operator inference.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Computer Science, Interdisciplinary Applications
Cong Xiao, Olwijn Leeuwenburgh, Hai Xiang Lin, Arnold Heemink
Summary: A reduced order modeling algorithm is proposed for estimating space varying parameter patterns in numerical models. Domain decomposition is used to construct separate approximations in each subdomain, with a new local parameterization to decouple computational cost from global principal components. This approach drastically reduces the number of full order simulations needed for deriving reduced order models, with optimal local parameter patterns projected onto global patterns to avoid non-smoothness at subdomain boundaries.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Kun Li, Ting-Zhu Huang, Liang Li, Stephane Lanteri
Summary: This paper presents a non-intrusive model order reduction (MOR) for solving parameterized electromagnetic scattering problems, where a database of full-order solution samples is prepared offline and the reduced solutions for new time and parameter values can be quickly recovered online. The method uses POD and CSI techniques to reduce computational complexity, ensuring the computational validity of the method, and constructs an efficient error estimator.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
