scholarly journals Model Order Reduction of Nonlinear Magnetodynamics with Manifold Interpolation

2015 ◽  
Author(s):  
Y. Paquay ◽  
O. Brüls ◽  
C. Geuzaine
Keyword(s):  
Model Order Reduction ◽  
Interpolation Method ◽  
Order Reduction ◽  
Nonlinear Problems ◽  
Single Shot ◽  
Reduced Basis ◽  
Model Order ◽  
Core System ◽  
Input Parameters ◽  
Speed Up

In the model order reduction community, linear systems have been widely studied and reduced thanks to various techniques. Proper Orthogonal Decomposition (POD) in particular has been very successful, and has recently been gaining popularity in computational electromagnetics. However, the efficiency of POD degrades considerably for nonlinear problems, in particular for nonlinear magnetodynamic models---necessary for designing most of today's electrical machines and drives. We propose to investigate an algorithm which first applies the POD to construct reduced order models of nonlinear magnetodynamic problems for discrete sets of values of the input parameters. Then, for a new set of values of the input parameters, a nonlinear interpolation on manifolds is performed to determine the reduced basis. This interpolation method is based on the theory previously studied for aerodynamic problems. The goal here is not to speed up single shot calculations, but to be able to determine efficiently reduced models for nonlinear problems based on previous offline computations. As a simple application, we apply the procedure to a nonlinear inductor-core system, solved using a classical finite element method. In order to gauge the interest of manifold interpolation we compare the proposed approach to the direct use of a precomputed reduced basis, as well as with the use of standard Lagrange interpolation.

Model of induction brazing of nonmagnetic metals using model order reduction approach

2018 ◽  
Vol 37 (4) ◽  
pp. 1515-1524 ◽  
Author(s):  
Pavel Karban ◽  
David Pánek ◽  
Ivo Doležel
Keyword(s):  
Heat Treatment ◽  
Model Order Reduction ◽  
Computation Time ◽  
Order Reduction ◽  
Nonlinear Problems ◽  
Model Order ◽  
Content Type ◽  
Weakly Nonlinear ◽  
Induction Brazing ◽  
Multiphysics Problems

Purpose A novel technique for control of complex physical processes based on the solution of their sufficiently accurate models is presented. The technique works with the model order reduction (MOR), which significantly accelerates the solution at a still acceptable uncertainty. Its advantages are illustrated with an example of induction brazing. Design/methodology/approach The complete mathematical model of the above heat treatment process is presented. Considering all relevant nonlinearities, the numerical model is reduced using the orthogonal decomposition and solved by the finite element method (FEM). It is cheap compared with classical FEM. Findings The proposed technique is applicable in a wide variety of linear and weakly nonlinear problems and exhibits a good degree of robustness and reliability. Research limitations/implications The quality of obtained results strongly depends on the temperature dependencies of material properties and degree of nonlinearities involved. In case of multiphysics problems characterized by low nonlinearities, the results of solved problems differ only negligibly from those solved on the full model, but the computation time is lower by two and more orders. Yet, however, application of the technique in problems with stronger nonlinearities was not fully evaluated. Practical implications The presented model and methodology of its solution may represent a basis for design of complex technologies connected with induction-based heat treatment of metal materials. Originality/value Proposal of a sophisticated methodology for solution of complex multiphysics problems established the MOR technology that significantly accelerates their solution at still acceptable errors.

scholarly journals Model order reduction for the simulation of parametric interest rate models in financial risk analysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andreas Binder ◽  
Onkar Jadhav ◽  
Volker Mehrmann
Keyword(s):  
Model Order Reduction ◽  
Financial Risk ◽  
Large Scale ◽  
Order Reduction ◽  
Parametric Models ◽  
Diffusion Reaction ◽  
High Dimensional ◽  
Reduced Basis ◽  
Model Order ◽  
Reduction Approach

AbstractThis paper presents a model order reduction approach for large scale high dimensional parametric models arising in the analysis of financial risk. To understand the risks associated with a financial product, one has to perform several thousand computationally demanding simulations of the model which require efficient algorithms. We establish a model reduction approach based on a variant of the proper orthogonal decomposition method to generate small model approximations for the high dimensional parametric convection-diffusion-reaction partial differential equations. This approach requires to solve the full model at some selected parameter values to generate a reduced basis. We propose an adaptive greedy sampling technique based on surrogate modeling for the selection of the sample parameter set. The new technique is analyzed, implemented, and tested on industrial data of a floater with cap and floor under the Hull–White model. The results illustrate that the reduced model approach works well for short-rate models.

scholarly journals Model Order Reduction Technique Applied on Harmonic Analysis of a Submerged Vibrating Blade

2019 ◽  
Vol 24 (1) ◽  
pp. 131-142 ◽  
Author(s):  
E. Tengs ◽  
F. Charrassier ◽  
M. Holst ◽  
Pål-Tore Storli
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Reduction Technique ◽  
Reduced Order Model ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Speed Up ◽  
Speedup Factor ◽  
Fully Coupled

Abstract As part of an ongoing study into hydropower runner failure, a submerged, vibrating blade is investigated both experimentally and numerically. The numerical simulations performed are fully coupled acoustic-structural simulations in ANSYS Mechanical. In order to speed up the simulations, a model order reduction technique based on Krylov subspaces is implemented. This paper presents a comparison between the full ANSYS harmonic response and the reduced order model, and shows excellent agreement. The speedup factor obtained by using the reduced order model is shown to be between one and two orders of magnitude. The number of dimensions in the reduced subspace needed for accurate results is investigated, and confirms what is found in other studies on similar model order reduction applications. In addition, experimental results are available for validation, and show good match when not too far from the resonance peak.

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