Stefanescu, RazvanSandu, AdrianNavon, I. M.2017-03-062017-03-062014-11-200271-2091http://hdl.handle.net/10919/75280This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree p. Such nonlinear terms have an on-line complexity of O(k^p+1), where k is the dimension of POD basis, and therefore is independent of full space dimension. However it is efficient only for quadratic nonlinear terms since for higher nonlinearities standard POD proves to be less time consuming once the POD basis dimension k is increased. Numerical experiments are carried out with a two dimensional shallow water equation (SWE) test problem to compare the performance of tensorial POD, standard POD, and POD/Discrete Empirical Interpolation Method (DEIM). Numerical results show that tensorial POD decreases by 76× times the computational cost of the on-line stage of standard POD for configurations using more than 300, 000 model variables. The tensorial POD SWE model was only 2 − 8× slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM shallow water equation model to compute its off-line stage faster than the standard and tensorial POD approaches.497 - 521 (25) page(s)enIn CopyrightTechnologyComputer Science, Interdisciplinary ApplicationsMathematics, Interdisciplinary ApplicationsMechanicsPhysics, Fluids & PlasmasComputer ScienceMathematicsPhysicstensorial proper orthogonal decomposition (POD)discrete empirical interpolation method (DEIM)reduced order models (ROMs)shallow water equations (SWE)finite difference methodsalternating direction implicit methods (ADI)PROPER ORTHOGONAL DECOMPOSITIONPARTIAL-DIFFERENTIAL-EQUATIONSDISCRETE EMPIRICAL INTERPOLATIONMODEL-REDUCTIONCOHERENT STRUCTURESDIFFUSION EQUATIONSGALERKIN PROJECTIONPARTIAL-REALIZATIONLYAPUNOV EQUATIONSFLUID-DYNAMICSArticle - Refereedhttps://doi.org/10.1002/fld.3946768