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Model reduction using the proper orthogonal decomposition (POD) method is applied to the dynamics of ferroelastic patches to study the first order square to rectangular phase transformations. Governing equations for the system dynamics are…

Materials Science · Physics 2007-05-23 Linxiang X. Wang , Roderick V. N. Melnik

Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…

Numerical Analysis · Mathematics 2023-08-08 Giuseppe Carere , Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza , Rob Stevenson

Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are two complementary singular-value decomposition (SVD) techniques that are widely used to construct reduced-order models (ROMs) in a variety of fields of science…

Numerical Analysis · Mathematics 2020-02-19 Hannah Lu , Daniel M. Tartakovsky

In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced…

Dynamical Systems · Mathematics 2013-12-17 Dan Yu , Suman Chakravorty

In electromagnetic analysis, the finite element and boundary element methods jointly known as 'FEM-BEM coupling' is applied for numerically solving levitation problem based on eddy current. The main focus behind this coupled analysis method…

Numerical Analysis · Mathematics 2021-08-24 Sayan Sarkar , Amit Jena , Mashuq un Nabi

This paper proposes a large eddy simulation reduced order model(LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition(POD) is used to define the ROM basis and a…

Fluid Dynamics · Physics 2015-10-12 Xuping Xie , David Wells , Zhu Wang , Traian Iliescu

We propose a reduced basis method to solve time-dependent partial differential equations based on the Laplace transform. Unlike traditional approaches, we start by applying said transform to the evolution problem, yielding a…

Numerical Analysis · Mathematics 2025-09-30 Ricardo Reyes

We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators and, especially, generalizes MFEM to…

Numerical Analysis · Mathematics 2020-10-30 Felix Black , Philipp Schulze , Benjamin Unger

This study explores reduced-order modeling for analyzing the time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in…

Computational Engineering, Finance, and Science · Computer Science 2024-06-18 Gopal Agarwal , Jorge-Humberto Urrea-Quintero , Henning Wessels , Thomas Wick

This paper puts forth several closure models for the proper orthogonal decomposition (POD) reduced order modeling of fluid flows. These new closure models, together with other standard closure models, are investigated in the numerical…

Fluid Dynamics · Physics 2018-01-29 Omer San , Traian Iliescu

We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from…

Numerical Analysis · Mathematics 2020-08-04 Carmen Gräßle , Michael Hinze , Stefan Volkwein

This paper deals with the development of a Reduced-Order Model (ROM) to investigate haemodynamics in cardiovascular applications. It employs the use of Proper Orthogonal Decomposition (POD) for the computation of the basis functions and the…

Numerical Analysis · Mathematics 2025-01-24 Pierfrancesco Siena , Pasquale Claudio Africa , Michele Girfoglio , Gianluigi Rozza

In this paper we utilize the Proper Orthogonal Decomposition (POD) method for model order reduction in application to Smoluchowski aggregation equations with source and sink terms. In particular, we show in practice that there exists a…

Numerical Analysis · Mathematics 2024-03-06 Ivan V. Timokhin , Sergey A. Matveev , Eugene E. Tyrtyshnikov , Alexander P. Smirnov

Temporal or spatial structures are readily extracted from complex data by modal decompositions like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). Subspaces of such decompositions serve as reduced order models…

Fluid Dynamics · Physics 2019-02-25 Jörn Sesterhenn , Amir Shahirpour

This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…

Numerical Analysis · Mathematics 2023-08-08 Efthymios N. Karatzas , Francesco Ballarin , Gianluigi Rozza

We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…

Numerical Analysis · Mathematics 2016-09-21 Sebastian Ullmann , Marko Rotkvic , Jens Lang

This paper puts forth two new closure models for the proper orthogonal decomposition reduced-order modeling of structurally dominated turbulent flows: the dynamic subgrid-scale model and the variational multiscale model. These models, which…

Computational Physics · Physics 2015-05-28 Zhu Wang , Imran Akhtar , Jeff Borggaard , Traian Iliescu

The finite-element analysis of three-dimensional magnetostatic problems in terms of magnetic vector potential has proven to be one of the most efficient tools capable of providing the excellent quality results but becoming computationally…

Computational Physics · Physics 2023-07-25 Alexander Chervyakov

Feedback control synthesis for nonlinear, parameter-dependent fluid flow control problems is considered. The optimal feedback law requires the solution of the Hamilton-Jacobi-Bellman (HJB) PDE suffering the curse of dimensionality. This is…

Optimization and Control · Mathematics 2023-11-29 Sergey Dolgov , Dante Kalise , Luca Saluzzi

We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…

Numerical Analysis · Mathematics 2021-07-21 Gerhard Kirsten