Haolun Zhang¹, Mengna Yang¹, Jie Wei², Yufeng Nie^2,*

Digital Engineering and Digital Twin, Vol.2, pp. 49-77, 2024, DOI:10.32604/dedt.2023.044180

Abstract This paper mainly considers the formulation and theoretical analysis of the reduced-order numerical method constructed by proper orthogonal decomposition (POD) for nonlocal diffusion problems with a finite range of nonlocal interactions. We first set up the classical finite element discretization for nonlocal diffusion equations and briefly explain the difference between nonlocal and partial differential equations (PDEs). Nonlocal models have to handle double integrals when using finite element methods (FEMs), which causes the generation of algebraic systems to be more challenging and time-consuming, and discrete systems have less sparsity than those for PDEs. So we establish a reduced-order model (ROM) for… More >

Heather Dillon^a , Ashley Emery^b,† , Ann Mescher^b

Frontiers in Heat and Mass Transfer, Vol.4, No.2, pp. 1-9, 2013, DOI:10.5098/hmt.v4.2.3004

Abstract A computational model is presented that extends prior work on unsteady natural convection in a tall rectangular cavity with aspect ratio 10 and applies Proper Orthogonal Decomposition to the results. The solution to the weakly compressible Navier-Stokes equation is computed for a range of Rayleigh numbers between 2 × 10⁷ and 2.2 × 10⁸ with Prandtl number 0.71. A detailed spectral analysis shows dynamic system behavior beyond the Hopf bifurcation that was not previously observed. The wider Rayleigh range reveals new dynamic system behavior for the rectangular geometry, specifically a return to a stable oscillatory behavior that was not predicted… More >

Loc Vu-Quoc^1,*, Alexander Humer²

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.2, pp. 1069-1343, 2023, DOI:10.32604/cmes.2023.028130

Abstract Three recent breakthroughs due to AI in arts and science serve as motivation: An award winning digital image, protein folding, fast matrix multiplication. Many recent developments in artificial neural networks, particularly deep learning (DL), applied and relevant to computational mechanics (solid, fluids, finite-element technology) are reviewed in detail. Both hybrid and pure machine learning (ML) methods are discussed. Hybrid methods combine traditional PDE discretizations with ML methods either (1) to help model complex nonlinear constitutive relations, (2) to nonlinearly reduce the model order for efficient simulation (turbulence), or (3) to accelerate the simulation by predicting certain components in the traditional… More >

Weimin Wu, Chuande Zhou^*

FDMP-Fluid Dynamics & Materials Processing, Vol.16, No.5, pp. 883-901, 2020, DOI:10.32604/fdmp.2020.010407

Abstract The behavior of the tip wake of a wind turbine is one of the hot issues in the wind power field. This problem can partially be tackled using Computational Fluid Dynamics (CFD). However, this approach lacks the ability to provide insights into the spatial structure of important high-order flows. Therefore, with the horizontal axis wind turbine as the main focus, in this work, firstly, we conduct CFD simulations of the wind turbine in order to obtain a data-driven basis relating to multiple working conditions for further analysis. Then, these data are studied using an extended Proper Orthogonal Decomposition (POD) algorithm.… More >

Arka Das¹, Anthony Khoury¹, Eduardo Divo^{1, *}, Victor Huayamave¹, Andres Ceballos², Ron Eaglin², Alain Kassab³, Adam Payne⁴, Vijay Yelundur⁴, Hubert Seigneur⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.3, pp. 757-777, 2020, DOI:10.32604/cmes.2020.08164

Abstract This paper presents a numerical reduced order model framework to simulate the physics of the thermomechanical processes that occur during c-Si photovoltaic (PV) cell fabrication. A response surface based on a radial basis function (RBF) interpolation network trained by a Proper Orthogonal Decomposition (POD) of the solution fields is developed for fast and accurate approximations of thermal loading conditions on PV cells during the fabrication processes. The outcome is a stand-alone computational tool that provides, in real time, the quantitative and qualitative thermomechanical response as a function of user-controlled input parameters for fabrication processes with the precision of 3D finite… More >

A. Rama Mohan Rao¹, K. Lakshmi¹, Karthik Ganesan²

Structural Durability & Health Monitoring, Vol.9, No.2, pp. 99-128, 2013, DOI:10.32604/sdhm.2013.009.099

Abstract Development of efficient system identification techniques is highly relevant for large civil infrastructure for effective health monitoring, damage detection and vibration control. This paper presents a system identification scheme in time domain to estimate stiffness and damping parameters of structures using measured acceleration. Instead of solving the system identification problem as an inverse problem, we formulate it as an optimisation problem. Particle swarm optimisation (PSO) and its other variants has been a subject of research for the past few decades for solving complex optimisation problems. In this paper, a dynamic quantum behaved particle swarm optimisation algorithm (DQPSO) is proposed for… More >

Dan Xie¹, Min Xu²

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 377-409, 2013, DOI:10.3970/cmes.2013.093.377

Abstract We apply a simple proper orthogonal decomposition (POD) method to compute the nonlinear oscillations of a degenerate two-dimensional fluttering plate undergoing supersonic flow. First, the von Karman’s large deflection theory and quasi-steady aerodynamic theory are employed in constructing the governing equations of the simply supported plate. Then, the governing equations are solved by both the Galerkin method and the POD method. The Galerkin method is accurate but sometimes computationally expensive, since the number of degrees of freedom (dofs) required is relatively large provided that nonlinearity is strong. The POD method can be used to capture the complex dynamics of a… More >

Montri Maleewong¹, Sirod Sirisup²

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.2, pp. 193-216, 2010, DOI:10.3970/cmes.2010.065.193

Abstract In this paper, we describe our investigation of an "on-line" POD-assisted projective integration method for solving a nonlinear PDE. Using the on-line method, we have computed the representative POD modes without assuming knowledge of the underlying slow manifold along the integration process. This approach is based on the "equation-free" framework where the governing PDE does not need to be projected onto the POD bases in order to build a reduced-order model. The main objectives of this study were to investigate the effectiveness of the method in reducing the computational time required for numerically solving a nonlinear PDE. Here, the one-dimensional… More >

Sanjay Mittal¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 63-78, 2008, DOI:10.3970/cmes.2008.027.063

Abstract Flow past a circular cylinder looses stability at a Reynolds number,Re~47. It has been shown, in the past, that the linear stability analysis (LSA) of the steady state solution can predict not only the critical Re, but also the non-dimensional frequency, St, of the associated instability. For larger Re the non-linear effects become important and the LSA of the steady-state flow does not predict the correct St. It is shown that, in general, the LSA applied to the time-averaged flow can result in useful information regarding its stability. This idea is applied to the Re = 100 flow past a… More >