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

Nonlinear model order reduction for the fast solution of induction heating problems in time-domain

2017 ◽  
Vol 36 (2) ◽  
pp. 469-475 ◽  
Author(s):  
Lorenzo Codecasa ◽  
Federico Moro ◽  
Piergiorgio Alotto
Keyword(s):  
Induction Heating ◽  
Model Order Reduction ◽  
Computing Time ◽  
Computational Cost ◽  
Order Reduction ◽  
Reduced Model ◽  
Problem Solution ◽  
Model Order ◽  
Content Type ◽  
Time Harmonic

Purpose This paper aims to propose a fast and accurate simulation of large-scale induction heating problems by using nonlinear reduced-order models. Design/methodology/approach A projection space for model order reduction (MOR) is quickly generated from the first kernels of Volterra’s series to the problem solution. The nonlinear reduced model can be solved with time-harmonic phasor approximation, as the nonlinear quadratic structure of the full problem is preserved by the projection. Findings The solution of induction heating problems is still computationally expensive, even with a time-harmonic eddy current approximation. Numerical results show that the construction of the nonlinear reduced model has a computational cost which is orders of magnitude smaller than that required for the solution of the full problem. Research limitations/implications Only linear magnetic materials are considered in the present formulation. Practical implications The proposed MOR approach is suitable for the solution of industrial problems with a computing time which is orders of magnitude smaller than that required for the full unreduced problem, solved by traditional discretization methods such as finite element method. Originality/value The most common technique for MOR is the proper orthogonal decomposition. It requires solving the full nonlinear problem several times. The present MOR approach can be built directly at a negligible computational cost instead. From the reduced model, magnetic and temperature fields can be accurately reconstructed in whole time and space domains.

Model Order Reduction of Visco-Thermal Acousto-Elastic Interaction in High-Pressure Centrifugal Compressors

2015 ◽  
Author(s):  
Jithin Jith ◽  
Sunetra Sarkar
Keyword(s):  
Finite Element ◽  
Supercritical Co2 ◽  
Model Order Reduction ◽  
Computational Cost ◽  
Order Reduction ◽  
Elastic Interaction ◽  
Computational Time ◽  
Centrifugal Impeller ◽  
Centrifugal Compressors ◽  
Model Order

Centrifugal compressors used in applications like enhanced oil recovery using gas re-injection and Carbon capture and sequestration operate at very high pressures and often have to to deal with supercritical CO2 which is considerably viscous. Increased viscosity leads to energy dissipation and introduces damping in the acousto-elastic interaction between supercritical CO2 and the impeller of a centrifugal compressor, thereby altering the frequency response of the system especially near resonant frequencies. In this paper, the damping introduced by visco-thermal effects in such acousto-elastic systems is accounted for in a numerically efficient manner. The acoustics in the fluid are modelled using the Boundary Layer Impedance (BLI) model and the centrifugal impeller as a linear elastic structure. The coupled acousto-elastic system is then solved using the finite element method. The finite element solution becomes computationally expensive especially when working with large three-dimensional models. In order to reduce the computational cost, a model order reduction technique based on a multi-point second-order Arnoldi (SOAR) procedure is developed. It is demonstrated that the reduced order model significantly brings down the computational time while being sufficiently accurate.

Model order reduction of nonlinear eddy-current field using parameterized CLN

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Miwa Tobita ◽  
Hamed Eskandari ◽  
Tetsuji Matsuo
Keyword(s):  
Model Order Reduction ◽  
Dynamical Behavior ◽  
Order Reduction ◽  
Parameter Variation ◽  
Computational Time ◽  
State Equations ◽  
Model Order ◽  
Content Type ◽  
Parameter Variations ◽  
Nonlinear State

Purpose The authors derive a nonlinear MOR based on the Cauer ladder network (CLN) representation, which serves as an application of the parameterized MOR. Two parametrized CLN representations were developed to handle the nonlinear magnetic field. Simulations using the parameterized CLN were also conducted using an iron-cored inductor model under the first-order approximation. Design/methodology/approach This work studies the effect of parameter variations on reduced systems and aims at developing a general formulation for parametrized model order reduction (MOR) methods with the dynamical transition of parameterized state. Findings Terms including time derivatives of basis vectors appear in nonlinear state equations, in addition to the linear network equations of the CLN method. The terms are newly derived by an exact formulation of the parameterized CLN and are named parameter variation terms in this study. According to the simulation results, the parameter variation terms play a significant role in the nonlinear state equations when reluctivity is used, while they can be neglected when differential reluctivity is used. Practical implications The computational time of nonlinear transient analyses can be greatly reduced by applying the parameterized CLN when the number of time steps is large. Originality/value The authors introduced a general representation for the dynamical behavior of the reduced system with time-varying parameters, which has not been theoretically discussed in previous studies. The effect of the parameter variations is numerically given as a form of parameter variation terms by the exact derivation of the nonlinear state equations. The influence of parameter variation terms was confirmed by simulation.

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