scholarly journals Advances in Hierarchical Model Reduction and combination with other computational reduction methods

2018 ◽  
Author(s):  
Giulia Meglioli ◽  
Matteo Zancanaro ◽  
Francesco Ballarin ◽  
Simona Perotto ◽  
Gianluigi Rozza
Keyword(s):  
Hierarchical Model ◽  
Computational Cost ◽  
Order Reduction ◽  
Reduced Basis ◽  
Element Discretization ◽  
Modal Expansion ◽  
Reduction Techniques ◽  
Computational Performance ◽  
Reduction Methods ◽  
Computational Reduction

In this work we present address the combination of the Hierarchical Model (Hi-Mod) reduction approach with projection-based reduced order methods, exploiting either on Greedy Reduced Basis (RB) or Proper Orthogonal Decomposition (POD), in a parametrized setting. The Hi-Mod approach, introduced in, is suited to reduce problems in pipe-like domains featuring a dominant axial dynamics, such as those arising for instance in haemodynamics. The Hi-Mod approach aims at reducing the computational cost by properly combining a finite element discretization of the dominant dynamics with a modal expansion in the transverse direction. In a parametrized context, the Hi-Mod approach has been employed as the high-fidelity method during the offline stage of model order reduction techniques based on RB or POD. The resulting combined reduction methods, which have been named Hi-RB and Hi-POD, respectively, will be presented with applications in diffusion-advection problems, fluid dynamics and optimal control problems, focusing on the approximation stability of the proposed methods and their computational performance.

(Generalized) Bloch mode synthesis for the fast dispersion curve calculation of 3D periodic metamaterials

2021 ◽  
Vol 263 (4) ◽  
pp. 2102-2113
Author(s):  
Vanessa Cool ◽  
Lucas Van Belle ◽  
Claus Claeys ◽  
Elke Deckers ◽  
Wim Desmet
Keyword(s):  
Dispersion Curve ◽  
Periodic Structures ◽  
Cell Model ◽  
Stop Band ◽  
Computational Cost ◽  
Order Reduction ◽  
Element Model ◽  
Unit Cell ◽  
Reduction Techniques ◽  
Bloch Mode

Metamaterials, i.e. artificial structures with unconventional properties, have shown to be highly potential lightweight and compact solutions for the attenuation of noise and vibrations in targeted frequency ranges, called stop bands. In order to analyze the performance of these metamaterials, their stop band behavior is typically predicted by means of dispersion curves, which describe the wave propagation in the corresponding infinite periodic structure. The input for these calculations is usually a finite element model of the corresponding unit cell. Most common in literature are 2D plane metamaterials, which often consist of a plate host structure with periodically added masses or resonators. In recent literature, however, full 3D metamaterials are encountered which are periodic in all three directions and which enable complete, omnidirectional stop bands. Although these 3D metamaterials have favorable vibro-acoustic characteristics, the computational cost to analyze them quickly increases with unit cell model size. Model order reduction techniques are important enablers to overcome this problem. In this work, the Bloch Mode Synthesis (BMS) and generalized BMS (GBMS) reduction techniques are extended from 2D to 3D periodic structures. Through several verifications, it is demonstrated that dispersion curve calculation times can be strongly reduced, while accurate stop band predictions are maintained.

scholarly journals Transient Dynamical-Thermal-Optical System Modeling and Simulation

2020 ◽  
Vol 238 ◽  
pp. 12001
Author(s):  
Luzia Hahn ◽  
Peter Eberhard
Keyword(s):  
Optical System ◽  
High Performance ◽  
System Modeling ◽  
Computational Cost ◽  
Order Reduction ◽  
Optical Systems ◽  
Model Order ◽  
Transient Simulations ◽  
Reduction Methods ◽  
Low Computational Cost

In this work, methods and procedures are investigated for the holistic simulation of the dynamicalthermal behavior of high-performance optics like lithography objectives. Flexible multibody systems in combination with model order reduction methods, finite element thermal analysis and optical system analyses are used for transient simulations of the dynamical-thermal behavior of optical systems at low computational cost.

Comparison of Model Order Reduction Methods in Thermoacoustic Stability Analysis

2021 ◽  
Author(s):  
Naman Purwar ◽  
Maximilian Meindl ◽  
Wolfgang Polifke
Keyword(s):  
Stability Analysis ◽  
Transfer Function ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Model Order ◽  
Reduction Techniques ◽  
Cavity Modes ◽  
Reduction Methods ◽  
Transfer Behavior ◽  
Modal Truncation

Abstract Model order reduction can play a pivotal role in reducing the cost of repeated computations of large thermoacoustic models required for comprehensive stability analysis and optimization. In this proof-of-concept study, acoustic wave propagation is modeled with a 1D network approach, while acoustic-flame interactions are modeled by a flame transfer function. Three reduction techniques are applied to the acoustic subsystem: firstly modal truncation based on preserving the acoustic eigenmodes, and then two approaches that strive to preserve the input-output transfer behavior of the acoustic subsystem, i.e., truncated balanced realization and iterative rational Krylov algorithm. After reduction, the reduced-order models (ROMs) are coupled with the flame transfer function. Results show that the coupled reduced system from modal truncation accurately captures thermoacoustic cavity modes with weak influence of the flame, but fails for cavity modes strongly influenced by the flame as well as for intrinsic thermoacoustic modes. On the contrary, the coupled ROMs generated with the other two methods accurately predict all types of modes. It is concluded that reduction techniques based on preserving transfer behavior are more suitable for thermoacoustic stability analysis.

scholarly journals Hyper-Reduction Over Nonlinear Manifolds for Large Nonlinear Mechanical Systems

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Shobhit Jain ◽  
Paolo Tiso
Keyword(s):  
Finite Element ◽  
Model Reduction ◽  
Computational Cost ◽  
Galerkin Projection ◽  
Dimensional Linear Subspace ◽  
Reduction Techniques ◽  
Energy Conserving ◽  
Reduction Methods ◽  
Wing Structure ◽  
Nonlinear Manifolds

Common trends in model reduction of large nonlinear finite element (FE)-discretized systems involve Galerkin projection of the governing equations onto a low-dimensional linear subspace. Though this reduces the number of unknowns in the system, the computational cost for obtaining the reduced solution could still be high due to the prohibitive computational costs involved in the evaluation of nonlinear terms. Hyper-reduction methods are then used for fast approximation of these nonlinear terms. In the finite element context, the energy conserving sampling and weighing (ECSW) method has emerged as an effective tool for hyper-reduction of Galerkin-projection-based reduced-order models (ROMs). More recent trends in model reduction involve the use of nonlinear manifolds, which involves projection onto the tangent space of the manifold. While there are many methods to identify such nonlinear manifolds, hyper-reduction techniques to accelerate computation in such ROMs are rare. In this work, we propose an extension to ECSW to allow for hyper-reduction using nonlinear mappings, while retaining its desirable stability and structure-preserving properties. As a proof of concept, the proposed hyper-reduction technique is demonstrated over models of a flat plate and a realistic wing structure, whose dynamics have been shown to evolve over a nonlinear (quadratic) manifold. An online speed-up of over one thousand times relative to the full system has been obtained for the wing structure using the proposed method, which is higher than its linear counterpart using the ECSW.

Separated Representations of Incremental Elastoplastic Simulations

2015 ◽  
Vol 651-653 ◽  
pp. 1285-1293 ◽  
Author(s):  
Mohamed Aziz Nasri ◽  
Jose Vicente Aguado ◽  
Amine Ammar ◽  
Elias Cueto ◽  
Francisco Chinesta ◽  
...  
Keyword(s):  
Model Order Reduction ◽  
Mechanical Systems ◽  
Order Reduction ◽  
Fast Simulation ◽  
Reduced Basis ◽  
Model Order ◽  
Reduction Techniques ◽  
Separated Representations ◽  
Separated Representation

Forming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems, however nonlinear history-dependent behaviors remain still today challenging scenarios for the application of these techniques. In this work we are proposing a quite simple non intrusive strategy able to address such behaviors by coupling a separated representation with a POD-based reduced basis within an incremental elastoplastic formulation.

scholarly journals Vibration of carbon nanotubes with defects: order reduction methods

2018 ◽  
Vol 474 (2211) ◽  
pp. 20170555 ◽  
Author(s):  
Robert B. Hudson ◽  
Alok Sinha
Keyword(s):  
Carbon Nanotubes ◽  
Periodic Structures ◽  
Order Reduction ◽  
Domain Analysis ◽  
Computational Effort ◽  
Mode Shapes ◽  
Mode Localization ◽  
Reduction Techniques ◽  
Reduction Methods ◽  
The Impact

Order reduction methods are widely used to reduce computational effort when calculating the impact of defects on the vibrational properties of nearly periodic structures in engineering applications, such as a gas-turbine bladed disc. However, despite obvious similarities these techniques have not yet been adapted for use in analysing atomic structures with inevitable defects. Two order reduction techniques, modal domain analysis and modified modal domain analysis, are successfully used in this paper to examine the changes in vibrational frequencies, mode shapes and mode localization caused by defects in carbon nanotubes. The defects considered are isotope defects and Stone–Wales defects, though the methods described can be extended to other defects.

Faster prediction of wildfire behaviour by physical models through application of proper orthogonal decomposition

2016 ◽  
Vol 25 (11) ◽  
pp. 1181 ◽  
Author(s):  
Elisa Guelpa ◽  
Adriano Sciacovelli ◽  
Vittorio Verda ◽  
Davide Ascoli
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Physical Model ◽  
Computational Cost ◽  
Computation Time ◽  
Order Reduction ◽  
Orthogonal Decomposition ◽  
Physical Models ◽  
Reduction Techniques ◽  
Rate Of Spread ◽  
Proper Orthogonal

Physical models of wildfires are of particular interest in fire behaviour research and have applications in firefighting, rescue and evacuation. However, physical models present a challenge as a result of the large computational resources they often require, especially for the analysis of large areas or when multiple scenarios are investigated. The objective of this paper is to explore the opportunity to reduce the computation time requested by physical wildfire models through application of a model order reduction technique, specifically the proper orthogonal decomposition (POD) technique. POD is here applied to a simple one-dimensional physical model. The full physical model for illustration of the concept is first tested with experimental data to check its ability to simulate wildfire behaviour; it is then reduced using the POD technique. It is shown that the reduced model is able to simulate fire propagation with only small deviations in results in comparison with the physical model (~6.4% deviation in the rate of spread, ROS) and a drastic reduction (~85%) in computational cost. The results demonstrate the advantages of applying effective reduction techniques to create new generations of fire models based on reduced physical approaches. The potential applicability of POD to more complex models is also discussed.

scholarly journals Model Order Reduction in Computational Multiscale Fracture Mechanics

2016 ◽  
Vol 713 ◽  
pp. 248-253
Author(s):  
M. Caicedo ◽  
J. Oliver ◽  
A.E. Huespe ◽  
O. Lloberas-Valls
Keyword(s):  
Model Order Reduction ◽  
High Performance ◽  
Computational Cost ◽  
Order Reduction ◽  
Cementitious Materials ◽  
Reduced Model ◽  
Computational Time ◽  
Strong Discontinuity ◽  
Model Order ◽  
Reduction Techniques

Nowadays, the model order reduction techniques have become an intensive research eld because of the increasing interest in the computational modeling of complex phenomena in multi-physic problems, and its conse- quent increment in high-computing demanding processes; it is well known that the availability of high-performance computing capacity is, in most of cases limited, therefore, the model order reduction becomes a novelty tool to overcome this paradigm, that represents an immediately challenge in our research community. In computational multiscale modeling for instance, in order to study the interaction between components, a di erent numerical model has to be solved in each scale, this feature increases radically the computational cost. We present a reduced model based on a multi-scale framework for numerical modeling of the structural failure of heterogeneous quasi-brittle materials using the Strong Discontinuity Approach (CSD). The model is assessed by application to cementitious materials. The Proper Orthogonal Decomposition (POD) and the Reduced Order Integration Cubature are the pro- posed techniques to develop the reduced model, these two techniques work together to reduce both, the complexity and computational time of the high-delity model, in our case the FE2 standard model

Comparison of Model Order Reduction Methods in Thermoacoustic Stability Analysis

2021 ◽  
Author(s):  
Naman Purwar ◽  
Maximilian Meindl ◽  
Wolfgang Polifke
Keyword(s):  
Stability Analysis ◽  
Transfer Function ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Model Order ◽  
Reduction Techniques ◽  
Cavity Modes ◽  
Reduction Methods ◽  
Transfer Behavior ◽  
Modal Truncation

Abstract Model order reduction can play a pivotal role in reducing the cost of repeated computations of large thermoacoustic models required for comprehensive stability analysis and optimization. In this proof-of-concept study, acoustic wave propagation is modeled with a 1D network approach, while acoustic-flame interactions are modeled by a flame transfer function. Three reduction techniques are applied to the acoustic subsystem: firstly modal truncation based on preserving the acoustic eigenmodes, and then two approaches that strive to preserve the input-output transfer behavior of the acoustic subsystem, i.e., truncated balanced realization and iterative rational Krylov algorithm. After reduction, the reduced-order models (ROMs) are coupled with the flame transfer function. Results show that the coupled reduced system from modal truncation accurately captures thermoacoustic cavity modes with weak influence of the flame, but fails for cavity modes strongly influenced by the flame as well as for intrinsic thermoacoustic modes. On the contrary, the coupled ROMs generated with the other two methods accurately predict all types of modes. It is concluded that reduction techniques based on preserving transfer behavior are more suitable for thermoacoustic stability analysis.

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