Algebraic and Parametric Solvers for the Power Flow Problem: Towards Real-Time and Accuracy-Guaranteed Simulation of Electric Systems

García-Blanco, Raquel; Dı́ez, Pedro; Borzacchiello, Domenico; Chinesta, Francisco

doi:10.1007/s11831-017-9223-6

Cited by 7 publications

(6 citation statements)

References 115 publications

(131 reference statements)

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“…51,56 Thus, it provides additional accuracy in the approximation of the viscous part of the drag with respect to classical primal finite element formulations, in which this is obtained as a postprocess of the computed velocity field. To construct separated approximations assessing the accuracy in a given quantity of interest, interested readers are referred to, 68,69 where PGD algorithms with goal-oriented error control were investigated.…”

Section: Devising Separated Response Surfacesmentioning

confidence: 99%

Separated response surfaces for flows in parametrised domains: comparison of a priori and a posteriori PGD algorithms

Giacomini,

Borchini,

Sevilla

et al. 2020

Preprint

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Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among them is not always a trivial task. This work presents a comparison of the performance of a priori and a posteriori proper generalised decomposition (PGD) algorithms for an incompressible Stokes flow problem in a geometrically parametrised domain. This problem is particularly challenging as the geometric parameters affect both the solution manifold and the computational spatial domain. The difficulty is further increased because multiple geometric parameters are considered and extended ranges of values are analysed for the parameters and this leads to significant variations in the flow features. Using a set of numerical experiments involving geometrically parametrised microswimmers, the two PGD algorithms are extensively compared in terms of their accuracy and their computational cost, expressed as a function of the number of full-order solves required.

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Section: Devising Separated Response Surfacesmentioning

confidence: 99%

Separated response surfaces for flows in parametrised domains: comparison of a priori and a posteriori PGD algorithms

Giacomini,

Borchini,

Sevilla

et al. 2020

Preprint

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show abstract

“…13: end while the problem under analysis, e.g. the norm of the residual of the governing equations or the goal-oriented estimate for a quantity of interest [44,72,73].…”

mentioning

confidence: 99%

“…Thus, it provides additional accuracy in the approximation of the viscous part of the drag with respect to classical primal finite element formulations, in which this is obtained as a postprocess of the computed velocity field. To construct separated approximations assessing the accuracy in a given quantity of interest, interested readers are referred to [44,72,73], where PGD algorithms with goal-oriented error control were investigated.…”

mentioning

confidence: 99%

Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms

Giacomini

Borchini

Sevilla

et al. 2021

Finite Elements in Analysis and Design

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“…With the obtained vademecum, fast-response and multi-query can be achieved in real-time simulations which are denoted as online phase. The power of PGD is demonstrated in many different fields, such as structural analysis Vidal et al [2012Vidal et al [ , 2014, structural optimisation Leygue and Verron [2010], Ammar et al [2014], Courard et al [2015], computational rheology Chinesta et al [2011a], computational fluid dynamics González et al [2013], , heat transfer Berger et al [2017], power supply system García-Blanco et al [2017], parameter identification Nadal et al [2015a] etc. Now we introduce briefly the basics of PGD, using the previously established concepts from RB methods.…”

Section: Reduced Order Modelling With Pgdmentioning

confidence: 99%

Simulation tools for biomechanical applications with PGD-based reduced order models

Zou¹

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Numerical simulation tools are generally used in all modern engineering fields, especially those having difficulties in performing large number of practical experiments, such as biomechanics. Among the computational methods, Finite Element (FE) is an essential tool. Nowadays, the fast-growing computational techniques, from the upgrading hardware to the emerging of novel algorithm, have already enabled extensive applications in biomechanics. For applications that require fast response and/or multiple queries, Reduced Order Modelling (ROM) methods have been developed based on existing methods such as FE, and have eventually enabled real-time numerical simulation for a large variety of engineering problems. In this thesis, several novel computational techniques are developed to explore the capability of Proper Generalised Decomposition (PGD), which is an important approach of ROM. To assess the usability of the PGD-based ROM for biomechanical applications, a real human femur bone is chosen to study its mechanical behaviour as an example. Standard image-based modelling procedure in biomechanics is performed to create an FE model which is then validated with in vitro experimental results. As a basis of this work, the medical image processing has to be performed, in order to generate an available FE model. This model is validated according to data collected from a previously performed \textit{in vitro} experimental test. The full procedure of image-based model generation and the validation of generated model is described in Chapter 2. As a major objective of this thesis, a non-intrusive scheme for the PGD framework is developed in Chapter 3. It is implemented using in-house developed Matlab (Mathworks, USA) code to conduct the PGD work flow, and calling Abaqus as an external solver for devised fictitious mechanical problems. The transformation of data from computed tomography (CT) image set to FE model including inhomogeneous material properties is subjected to some physical constraints, and when applying the load, there are also geometric constraints limiting the locations where load could be applied. These constraints will lead to a constrained parameter space, which possibly has difficulty to be separated in a Cartesian fashion. Therefore, a novel strategy to separate the parameters in a collective manner is proposed in Chapter 4. Chapter 5 details a comprehensive application in biomechanics, the methodologies proposed in Chapter 3 and 4 are applied on the practical model generated in Chapter 2. As a typical application of the PGD vademecum, a material property identification problem is discussed. Further PGD vademecum is generated using the identified material properties with variable loading locations, and with this vademecum, real-time mechanical response of the femur is available. In addition, for the purpose of extending the methodologies to orthotropic materials, which is commonly used in biomechanics, in Chapter 6 another linear elastic model is investigated with the non-intrusive PGD scheme. Nowadays, isogeometric analysis (IGA) is a very popular tool in computational mechanics. It is appealing to take advantage of non-uniform rational B-splines (NURBS) to discretise the model. For PGD, using B-splines for the discretisation of the parameter space could improve the quality of vademecum, especially for problems involving sensitivities with respect to the parameters during the online computations. It is important and necessary to extend the PGD framework to nonlinear solid mechanics, because most biological soft tissues have been observed nonlinear mechanical behaviours. Consequently, in Chapter 7 we have developed a PGD framework for the St.Venant-Kirchhoff constitutive model using the Picard linearisation which is consistent with the fixed-point iteration algorithm commonly used in PGD. In Chapter 8, conclusive remarks are addressed as well as forecasts of possible future works.

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Algebraic and Parametric Solvers for the Power Flow Problem: Towards Real-Time and Accuracy-Guaranteed Simulation of Electric Systems

Cited by 7 publications

References 115 publications

Separated response surfaces for flows in parametrised domains: comparison of a priori and a posteriori PGD algorithms

Separated response surfaces for flows in parametrised domains: comparison of a priori and a posteriori PGD algorithms

Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms

Simulation tools for biomechanical applications with PGD-based reduced order models

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