scholarly journals The use of POD–DEIM model order reduction for the simulation of nonlinear hygrothermal problems

2020 ◽  
Vol 172 ◽  
pp. 04002
Author(s):  
Tianfeng Hou ◽  
Karl Meerbergen ◽  
Staf Roels ◽  
Hans Janssen
Keyword(s):  
Interpolation Method ◽  
Computational Cost ◽  
Order Reduction ◽  
Illustrative Case ◽  
Hygrothermal Simulation ◽  
Discrete Empirical Interpolation Method ◽  
Empirical Interpolation Method ◽  
Illustrative Case Study ◽  
Volume Method ◽  
Proper Orthogonal

In this paper, the discrete empirical interpolation method (DEIM) and the proper orthogonal decomposition (POD) method are combined to construct a reduced order model to lessen the computational expense of hygrothermal simulation. To investigate the performance of the POD-DEIM model, HAMSTAD benchmark 2 is selected as the illustrative case study. To evaluate the accuracy of the POD-DEIM model as a function of the number of construction modes and interpolation points, the results of the POD-DEIM model are compared with a POD and a Finite Volume Method (FVM). Also, as the number of construction modes/interpolation points cannot entirely represent the computational cost of different models, the accuracies of the different models are compared as function of the calculation time, to provide a fair comparison of their computational performances. Further, the use of POD-DEIM to simulate a problem different from the training snapshot simulation is investigated. The outcomes show that with a sufficient number of construction modes and interpolation points the POD-DEIM model can provide an accurate result, and is capable of reducing the computational cost relative to the POD and FVM.

scholarly journals Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equation

2016 ◽  
Author(s):  
Bulent Karasozen ◽  
Murat Uzunca ◽  
Tugba Kucukseyhan
Keyword(s):  
Interpolation Method ◽  
Computational Cost ◽  
Order Reduction ◽  
Euler Method ◽  
Order Model ◽  
Backward Euler ◽  
Discrete Empirical Interpolation Method ◽  
Dg Method ◽  
Empirical Interpolation Method ◽  
Proper Orthogonal

We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) equation. The FHN equation is discretized in space by the discontinuous Galerkin (dG) method and in time by the backward Euler method. Applying POD-DEIM (discrete empirical interpolation method) to the full order model (FOM) for different values of the parameter in the bistable nonlinearity, we show that using few POD and DEIM modes, the patterns can be computed accurately. Due to the local nature of the dG discretization, the PODDEIM requires less number of connected nodes than continuous finite element for the nonlinear terms, which leads to a significant reduction of the computational cost for dG POD-DEIM.

A Modified Discrete Empirical Interpolation Method for Reducing Non-Linear Structural Finite Element Models

2013 ◽  
Author(s):  
Paolo Tiso ◽  
Rob Dedden ◽  
Daniel Rixen
Keyword(s):  
Finite Element ◽  
Interpolation Method ◽  
Computational Cost ◽  
Order Reduction ◽  
Galerkin Projection ◽  
Alternative Formulation ◽  
Discrete Empirical Interpolation Method ◽  
Empirical Interpolation Method ◽  
The Cost ◽  
Discrete Empirical Interpolation

Model Order Reduction (MOR) in nonlinear structural analysis problems in usually carried out by a Galerkin projection of the primary variables on a sensibly smaller space. However, the cost of computing the nonlinear terms is still of the order of the full system. The Discrete Empirical Interpolation Method (DEIM) is an effective algorithm to reduce the computational cost of the nonlinear terms of the discretized governing equations. However, its efficiency is diminished when applied to a Finite Element (FE) framework. We present here an alternative formulation of the DEIM that suits FE discretized problems and preserves the efficiency and the accuracy of the original DEIM method.

REDUCED-ORDER MODELS FOR THE IMPLIED VARIANCE UNDER LOCAL VOLATILITY

2014 ◽  
Vol 17 (08) ◽  
pp. 1450053
Author(s):  
EKKEHARD W. SACHS ◽  
MARINA SCHNEIDER
Keyword(s):  
Implied Volatility ◽  
Interpolation Method ◽  
Order Reduction ◽  
Parabolic Partial Differential Equation ◽  
Local Volatility ◽  
Reduced Order ◽  
Reduction Techniques ◽  
Discrete Empirical Interpolation Method ◽  
Pros And Cons ◽  
Empirical Interpolation Method

Implied volatility is a key value in financial mathematics. We discuss some of the pros and cons of the standard ways to compute this quantity, i.e. numerical inversion of the well-known Black–Scholes formula or asymptotic expansion approximations, and propose a new way to directly calculate the implied variance in a local volatility framework based on the solution of a quasilinear degenerate parabolic partial differential equation. Since the numerical solution of this equation may lead to large nonlinear systems of equations and thus high computation times compared to the classical approaches, we apply model order reduction techniques to achieve computational efficiency. Our method of choice for the derivation of a reduced-order model (ROM) will be proper orthogonal decomposition (POD). This strategy is additionally combined with the discrete empirical interpolation method (DEIM) to deal with the nonlinear terms. Numerical results prove the quality of our approach compared to other methods.

scholarly journals Application of multiphysics model order reduction to doppler/neutronic feedback

2019 ◽  
Vol 5 ◽  
pp. 17 ◽  
Author(s):  
Peter German ◽  
Jean C. Ragusa ◽  
Carlo Fiorina
Keyword(s):  
Interpolation Method ◽  
Input Parameter ◽  
Order Reduction ◽  
Latin Hypercube Sampling ◽  
Order Model ◽  
Continuity Equations ◽  
Discrete Empirical Interpolation Method ◽  
Empirical Interpolation Method ◽  
Efficient Coupling ◽  
State Models

In this paper, a proper orthogonal decomposition based reduced-order model is presented for parametrized multiphysics computations. Our application physics is Doppler feedback in a simplified model of the molten salt fast reactor concept. The reduced model is created using the method of snapshots where the offline training set is obtained by exercising a full-order model created with the OpenFOAM based multiphysics solver, GeN-Foam. The steady state models solve the multi-group diffusion k-eigenvalue equations with moving precursors together with the energy equation. A fixed velocity field is assumed throughout the computations, hence the momentum and continuity equations are not solved. The discrete empirical interpolation method is used for the efficient coupling of the ROM solvers, while the input parameter space is surveyed using the improved distributed latin hypercube sampling algorithm.

Reduced-order models for radiative heat transfer of hypersonic vehicles

2020 ◽  
Vol 234 (11) ◽  
pp. 1836-1848
Author(s):  
Xiaoxuan Yan ◽  
Jinglong Han ◽  
Haiwei Yun ◽  
Xiaomao Chen
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Interpolation Method ◽  
Reduced Order Modeling ◽  
Orthogonal Decomposition ◽  
Hypersonic Vehicles ◽  
Reduced Order ◽  
Discrete Empirical Interpolation Method ◽  
Empirical Interpolation Method ◽  
Proper Orthogonal ◽  
Discrete Empirical Interpolation

Aerothermoelastic analysis of hypersonic vehicles is a complex multidisciplinary coupling problem. Thus, accurate modeling of varying disciplines with low computational cost is necessary. This work developed a tractable approach-based reduced-order modeling technology to solve the radiative thermal transfer problem in a hypersonic simulation. A method that combines proper orthogonal decomposition and unassembled discrete empirical interpolation method is developed to construct the reduced-order modeling. First, high-dimensional original systems are projected on the optional basis generated by proper orthogonal decomposition, and the nonlinear term is further approximated by unassembled discrete empirical interpolation method. Then, a numerical integration method for the solution of the reduced system of nonlinear differential equations is provided. Case studies that use a classical hypersonic control surface model, in which the time history and spatial distribution of the thermal load are known a priori, are conducted to validate the accuracy and efficiency of the reduced-order modeling methodology and to assess the robustness of the reduced-order modeling for thermal solution. Results indicate the ability of reduced-order modeling to reduce the nonlinear system size with reasonable accuracy.

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