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Article Citation - WoS: 4Citation - Scopus: 4Multi Input Dynamical Modeling of Heat Flow With Uncertain Diffusivity Parameter(Taylor & Francis inc, 2003) Efe, MÖ; Özbay, HThis paper focuses on the multi-input dynamical modeling of one-dimensional heat conduction process with uncertainty on thermal diffusivity parameter. Singular value decomposition is used to extract the most significant modes. The results of the spatiotemporal decomposition have been used in cooperation with Galerkin projection to obtain the set of ordinary differential equations, the solution of which synthesizes the temporal variables. The spatial properties have been generalized through a series of test cases and a low order model has been obtained. Since the value of the thermal diffusivity parameter is not known perfectly, the obtained model contains uncertainty. The paper describes how the uncertainty is modeled and how the boundary conditions are separated from the remaining terms of the dynamical equations. The results have been compared with those obtained through analytic solution.Article Citation - WoS: 64Citation - Scopus: 100Improved Routh-Pade Approximants: a Computer-Aided Approach(Ieee-inst Electrical Electronics Engineers inc, 2004) Singh, V; Chandra, D; Kar, HA geometric programming based computer-aided method to derive a reduced order (rth-order) approximant for a given (stable) SISO linear continuous-time system is presented. In this method, stability and the first r time moments/Markov parameters are preserved as well as the errors between a set of subsequent time moments/Markov parameters of the system and those of the model are minimized.Article Citation - WoS: 3Citation - Scopus: 5Global Energy Preserving Model Reduction for Multi-Symplectic Pdes(Elsevier Science inc, 2023) Uzunca, Murat; Karasozen, Bulent; Aydin, AyhanMany Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced -order model (ROM) for multi-symplectic Hamiltonian partial differential equations (PDEs) that preserves the global energy. The full-order solutions are obtained by finite difference discretization in space and the global energy preserving average vector field (AVF) method. The ROM is constructed in the same way as the full-order model (FOM) applying proper orthogonal decomposition (POD) with the Galerkin projection. The reduced-order system has the same structure as the FOM, and preserves the discrete reduced global energy. Ap-plying the discrete empirical interpolation method (DEIM), the reduced-order solutions are computed efficiently in the online stage. A priori error bound is derived for the DEIM ap-proximation to the nonlinear Hamiltonian. The accuracy and computational efficiency of the ROMs are demonstrated for the Korteweg de Vries (KdV) equation, Zakharov-Kuznetzov (ZK) equation, and nonlinear Schrodinger (NLS) equation in multi-symplectic form. Preser-vation of the reduced energies shows that the reduced-order solutions ensure the long-term stability of the solutions.(c) 2022 Elsevier Inc. All rights reserved.
