Acceleration techniques for reduced-order models based on proper orthogonal decomposition

Cizmas, Paul G. A.; Richardson, B.; Brenner, Thomas A.; O’Brien, Thomas J.; Breault, Ronald W.

doi:10.1016/j.jcp.2008.04.036

Cited by 28 publications

(17 citation statements)

References 24 publications

(38 reference statements)

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“…In other words, we do intend to approximate not only attractors but also transients. Our method can also be seen as a way to accelerate any NC (see [6] for an alternative acceleration procedure based on POD methods) by combining the use of the NC itself with that of the GS, as in the method proposed in [19]; also, as in [19], we do not restrict ourselves to polynomial nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

Reduced order models based on local POD plus Galerkin projection

Rapún

Vega

2010

Journal of Computational Physics

106

101

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A method is presented to accelerate numerical simulations on parabolic problems using a numerical code and a Galerkin system (obtained vía POD plus Galerkin projection) on a sequence of interspersed intervals. The lengths of these intervals are chosen according to several basic ideas that include an a priori estímate of the error of the Galerkin approximation. Several improvements are introduced that reduce computational complexity and deal with: (a) updating the POD manifold (instead of calculating it) at the end of each Galerkin interval; (b) using only a limited number of mesh points to calcúlate the right hand side of the Galerkin system; and (c) introducing a second error estímate based on a second Galerkin system to account for situations in which qualitative changes in the dynamics occur during the application of the Galerkin system. The resulting method, called local POD plus Galerkin projection method, turns out to be both robust and efficient. For illustration, we consider a time-dependent Fisher-like equation and a complex Ginzburg-Landau equation.

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Section: Introductionmentioning

confidence: 99%

Reduced order models based on local POD plus Galerkin projection

Rapún

Vega

2010

Journal of Computational Physics

106

101

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“…In the near future this paper will be submitted to a peer-reviewed journal for archival publication. The paper titled "Acceleration techniques for reduced-order models based on proper orthogonal decomposition" was published in in the Journal of Computational Physics, volume 227 (Cizmas et al, 2008). This paper presents the ROM based on POD used to solve the void fraction.…”

Section: Dissemination Of Research Resultsmentioning

confidence: 99%

“…The algorithm proposed herein for solving a system of equations Ax = b, in which the matrix A must be positive definite and quasi-symmetrical, begins by splitting the matrix into a symmetrical and a non-symmetrical part (Cizmas et al, 2008):…”

Section: Acceleration Methods For the Rommentioning

confidence: 99%

See 1 more Smart Citation

A Reduced-Order Model of Transport Phenomena for Power Plant Simulation

Cizmas¹,

Richardson²,

Brenner³

et al. 2009

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This report summarizes the objectives and tasks of this project, and describes how they were achieved. The report presents the progress made towards the program milestones and deliverables and summarizes the additional work done in the pursuit of these goals.A reduced-order model based on proper orthogonal decomposition (POD) has been developed to simulate transient two-and three-dimensional isothermal and non-isothermal flows in a fluidized bed. Reduced-order models of void fraction, gas and solids temperatures, granular energy, and z-direction gas and solids velocity have been added to the previous version of the code. These algorithms are presented and their implementation is discussed. Verification studies are presented for each algorithm.A number of methods to accelerate the computations performed by the reduced-order model are presented. The errors associated with each acceleration method are computed and discussed. Using a combination of acceleration methods, a two-dimensional isothermal simulation using the reduced-order model is shown to be 114 times faster than using the full-order model.In the pursue of achieving the objectives of the project and completing the tasks planned for this program, several unplanned and unforeseen results, methods and studies have been generated. These additional accomplishments are also presented and they include: (1) a study of the effect of snapshot sampling time on the computation of the POD basis functions, (2) an investigation of different strategies for generating the autocorrelation matrix used to find the POD basis functions, (3) the development and implementation of a bubble detection and tracking algorithm based on mathematical morphology, (4) a method for augmenting the proper orthogonal decomposition to better capture flows with discontinuities, such as bubbles, and (5) a mixed reduced-order/full-order model, called point-mode proper orthogonal decomposition, designed to avoid unphysical due to approximation errors.The limitations of the proper orthogonal decomposition method in simulating transient flows with moving discontinuities, such as bubbling flows, are discussed and several methods are proposed to adapt the method for future use.

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“…This factor suggests the potential savings that could be achieved using this method. In a different work, Cizmas et al [2] have explored several acceleration techniques based on POD. Basically, the techniques include a splitting of the snapshots datábase, which only require solving quasi-symmetrical matrices, and a strategy to reduce the frequency of projection.…”

Section: Introductionmentioning

confidence: 99%

A method to generate computationally efficient reduced order models

Alonso

Velázquez

Vega

2009

Computer Methods in Applied Mechanics and Engineering

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ARTICLE INFO ABSTRACT Keywords: Reduced order model Proper Orthogonal Decomposition Incompressible nonisothermal flowA new method is presented to genérate reduced order models (ROMs) in Fluid Dynamics problems. The method is based on the expansión of the flow variables on a Proper Orthogonal Decomposition (POD) basis, calculated from a limited number of snapshots, which are obtained via Computational Fluid Dynamics (CFD). Then, the POD-mode amplitudes are calculated as minimizers of a properly defined overall residual of the equations and boundary conditions. The residual can be calculated using only a limited number of points in the flow field, which can be scattered either all over the whole computational domain or over a smaller projection window. This means that the process is both computationally efficient (reconstructed flow fields require less than 1% of the time needed to compute a full CFD solution) and flexible (the projection window can avoid regions of large localized CFD errors). Also, various definitions of the residual are briefly discussed, along with the number and distribution of snapshots, the number of retained modes, and the effect of CFD errors, to conclude that the method is numerically robust. This is because the results are largely insensitive to the definition of the residual, to CFD errors, and to the CFD method itself, which may contain artificial stabilizing terms. Thus, the method is amenable for practical engineering applications.

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Acceleration techniques for reduced-order models based on proper orthogonal decomposition

Cited by 28 publications

References 24 publications

Reduced order models based on local POD plus Galerkin projection

Reduced order models based on local POD plus Galerkin projection

A Reduced-Order Model of Transport Phenomena for Power Plant Simulation

A method to generate computationally efficient reduced order models

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