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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 20 Jun 2021 20:12:14 GMT2021-06-20T20:12:14ZComparison of DEIM and BPIM to Speed up a POD-based Nonlinear Magnetostatic Model
http://hdl.handle.net/10985/11757
Comparison of DEIM and BPIM to Speed up a POD-based Nonlinear Magnetostatic Model
HENNERON, Thomas; MONTIER, Laurent; PIERQUIN, Antoine; CLENET, Stéphane
Proper Orthogonal Decomposition (POD) has been successfully used to reduce the size of linear Finite Element (FE) problems, and thus the computational time associated with. When considering a nonlinear behavior law of the ferromagnetic materials, the POD is not so efficient due to the high computational cost associated to the nonlinear entries of the full FE model. Then, the POD approach must be combined with an interpolation method to efficiently deal with the nonlinear terms, and thus obtaining an efficient reduced model. An interpolation method consists in computing a small number of nonlinear entries and interpolating the other terms. Different methods have been presented to select the set of nonlinear entries to be calculated. Then, the (Discrete) Empirical Interpolation method ((D)EIM) and the Best Points Interpolation Method (BPIM) have been developed. In this article, we propose to compare two reduced models based on the POD-(D)EIM and on the POD-BPIM in the case of nonlinear magnetostatics coupled with electric equation.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/117572017-01-01T00:00:00ZHENNERON, ThomasMONTIER, LaurentPIERQUIN, AntoineCLENET, StéphaneProper Orthogonal Decomposition (POD) has been successfully used to reduce the size of linear Finite Element (FE) problems, and thus the computational time associated with. When considering a nonlinear behavior law of the ferromagnetic materials, the POD is not so efficient due to the high computational cost associated to the nonlinear entries of the full FE model. Then, the POD approach must be combined with an interpolation method to efficiently deal with the nonlinear terms, and thus obtaining an efficient reduced model. An interpolation method consists in computing a small number of nonlinear entries and interpolating the other terms. Different methods have been presented to select the set of nonlinear entries to be calculated. Then, the (Discrete) Empirical Interpolation method ((D)EIM) and the Best Points Interpolation Method (BPIM) have been developed. In this article, we propose to compare two reduced models based on the POD-(D)EIM and on the POD-BPIM in the case of nonlinear magnetostatics coupled with electric equation.Structure Preserving Model Reduction of Low Frequency Electromagnetic Problem based on POD and DEIM
http://hdl.handle.net/10985/11758
Structure Preserving Model Reduction of Low Frequency Electromagnetic Problem based on POD and DEIM
MONTIER, Laurent; PIERQUIN, Antoine; HENNERON, Thomas; CLÉNET, Stéphane
The Proper Orthogonal Decomposition (POD) combined with the (Discrete) Empirical Interpolation Method (DEIM) can be used to reduce the computation time of the solution of a Finite Element (FE) model. However, it can lead to numerical instabilities. To increase the robustness, the POD_DEIM model must be constructed by preserving the structure of the full FE model. In this article, the structure preserving is applied for different potential formulations used to solve electromagnetic problems.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/117582017-01-01T00:00:00ZMONTIER, LaurentPIERQUIN, AntoineHENNERON, ThomasCLÉNET, StéphaneThe Proper Orthogonal Decomposition (POD) combined with the (Discrete) Empirical Interpolation Method (DEIM) can be used to reduce the computation time of the solution of a Finite Element (FE) model. However, it can lead to numerical instabilities. To increase the robustness, the POD_DEIM model must be constructed by preserving the structure of the full FE model. In this article, the structure preserving is applied for different potential formulations used to solve electromagnetic problems.Benefits of Waveform Relaxation Method and Output Space Mapping for the Optimization of Multirate Systems
http://hdl.handle.net/10985/7814
Benefits of Waveform Relaxation Method and Output Space Mapping for the Optimization of Multirate Systems
PIERQUIN, Antoine; BRISSET, Stéphane; HENNERON, Thomas; CLENET, Stéphane
We present an optimization problem that requires to model a multirate system, composed of subsystems with different time constants. We use waveform relaxation method in order to simulate such a system. But computation time can be penalizing in an optimization context. Thus we apply output space mapping which uses several models of the system to accelerate optimization. Waveform relaxation method is one of the models used in output space mapping.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/78142014-01-01T00:00:00ZPIERQUIN, AntoineBRISSET, StéphaneHENNERON, ThomasCLENET, StéphaneWe present an optimization problem that requires to model a multirate system, composed of subsystems with different time constants. We use waveform relaxation method in order to simulate such a system. But computation time can be penalizing in an optimization context. Thus we apply output space mapping which uses several models of the system to accelerate optimization. Waveform relaxation method is one of the models used in output space mapping.Model-Order Reduction of Magnetoquasi-Static Problems Based on POD and Arnoldi-Based Krylov Methods
http://hdl.handle.net/10985/9558
Model-Order Reduction of Magnetoquasi-Static Problems Based on POD and Arnoldi-Based Krylov Methods
PIERQUIN, Antoine; HENNERON, Thomas; CLENET, Stéphane; BRISSET, Stéphane
The proper orthogonal decomposition method and Arnoldi-based Krylov projection method are investigated in order to reduce a finite-element model of a quasi-static problem. Both methods are compared on an academic example in terms of computation time and precision.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/95582015-01-01T00:00:00ZPIERQUIN, AntoineHENNERON, ThomasCLENET, StéphaneBRISSET, StéphaneThe proper orthogonal decomposition method and Arnoldi-based Krylov projection method are investigated in order to reduce a finite-element model of a quasi-static problem. Both methods are compared on an academic example in terms of computation time and precision.Multirate coupling of controlled rectifier and non-linear finite element model based on Waveform Relaxation Method
http://hdl.handle.net/10985/10556
Multirate coupling of controlled rectifier and non-linear finite element model based on Waveform Relaxation Method
HENNERON, Thomas; CLENET, Stéphane; PIERQUIN, Antoine; BRISSET, Stéphane
To study a multirate system, each subsystem can be solved by a dedicated sofware with respect to the physical problem and the time constant. Then, the problem is the coupling of the solutions of the subsystems. The Waveform Relaxation Method (WRM) seems to be an interesting solution for the coupling but until now it has been mainly applied on academic examples. In this paper, the WRM is applied to perform the coupling of a controlled rectifier and a non-linear finite element model of a transformer.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/105562016-01-01T00:00:00ZHENNERON, ThomasCLENET, StéphanePIERQUIN, AntoineBRISSET, StéphaneTo study a multirate system, each subsystem can be solved by a dedicated sofware with respect to the physical problem and the time constant. Then, the problem is the coupling of the solutions of the subsystems. The Waveform Relaxation Method (WRM) seems to be an interesting solution for the coupling but until now it has been mainly applied on academic examples. In this paper, the WRM is applied to perform the coupling of a controlled rectifier and a non-linear finite element model of a transformer.Optimisation process to solve multirate system
http://hdl.handle.net/10985/16567
Optimisation process to solve multirate system
PIERQUIN, Antoine; HENNERON, Thomas; CLENET, Stéphane; BRISSET, Stephane
The modelling of a multirate system -composed of components with heterogeneous time constants- can be done using fixed-point method. This method allows a time-discretization of each subsystem with respect to its own time constant. In an optimisation process, executing the loop of the fixed-point at each model evaluation can be time consuming. By adding one of the searched waveform of the system to the optimisation variables, the loop can be avoided. This strategy is applied to the optimisation of a transformer.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/165672015-01-01T00:00:00ZPIERQUIN, AntoineHENNERON, ThomasCLENET, StéphaneBRISSET, StephaneThe modelling of a multirate system -composed of components with heterogeneous time constants- can be done using fixed-point method. This method allows a time-discretization of each subsystem with respect to its own time constant. In an optimisation process, executing the loop of the fixed-point at each model evaluation can be time consuming. By adding one of the searched waveform of the system to the optimisation variables, the loop can be avoided. This strategy is applied to the optimisation of a transformer.Mesh Deformation Based on Radial Basis Function Interpolation Applied to Low-Frequency Electromagnetic Problem
http://hdl.handle.net/10985/16535
Mesh Deformation Based on Radial Basis Function Interpolation Applied to Low-Frequency Electromagnetic Problem
HENNERON, Thomas; PIERQUIN, Antoine; CLENET, Stéphane
In order to take into account a modification of the geometry during an optimization process or due to a physical phenomenon, a deformation of the elements of the spatial discretization is preferable to conserve a conformal mesh and to apply the Finite Element (FE) method. To perform the displacement of nodes, interpolation method can be investigated in this context. In this paper, the Radial Basis Function (RBF) interpolation method is applied for low frequency electromagnetic problems solved by the FE method.. A 2D magnetostatic example is considered to study the influence of the parameters of the RBF interpolation. To test the extension in 3D, a non destructive testing (NDT) problem is treated where the shape of the crack is modified by applying the proposed method.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/165352019-01-01T00:00:00ZHENNERON, ThomasPIERQUIN, AntoineCLENET, StéphaneIn order to take into account a modification of the geometry during an optimization process or due to a physical phenomenon, a deformation of the elements of the spatial discretization is preferable to conserve a conformal mesh and to apply the Finite Element (FE) method. To perform the displacement of nodes, interpolation method can be investigated in this context. In this paper, the Radial Basis Function (RBF) interpolation method is applied for low frequency electromagnetic problems solved by the FE method.. A 2D magnetostatic example is considered to study the influence of the parameters of the RBF interpolation. To test the extension in 3D, a non destructive testing (NDT) problem is treated where the shape of the crack is modified by applying the proposed method.Surrogate Model Based on the POD Combined With the RBF Interpolation of Nonlinear Magnetostatic FE Model
http://hdl.handle.net/10985/17731
Surrogate Model Based on the POD Combined With the RBF Interpolation of Nonlinear Magnetostatic FE Model
HENNERON, Thomas; PIERQUIN, Antoine; CLENET, Stéphane
The Proper Orthogonal Decomposition (POD) is an interesting approach to compress into a reduced basis numerous solutions obtained from a parametrized Finite Element (FE) model. In order to obtain a fast approximation of a FE solution, the POD can be combined with an interpolation method based on Radial Basis Functions (RBF) to interpolate the coordinates of the solution into the reduced basis. In this paper, this POD-RBF approach is applied to a nonlinear magnetostatic problem and is used with a single phase transformer and a three-phase inductance.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/177312020-01-01T00:00:00ZHENNERON, ThomasPIERQUIN, AntoineCLENET, StéphaneThe Proper Orthogonal Decomposition (POD) is an interesting approach to compress into a reduced basis numerous solutions obtained from a parametrized Finite Element (FE) model. In order to obtain a fast approximation of a FE solution, the POD can be combined with an interpolation method based on Radial Basis Functions (RBF) to interpolate the coordinates of the solution into the reduced basis. In this paper, this POD-RBF approach is applied to a nonlinear magnetostatic problem and is used with a single phase transformer and a three-phase inductance.Structure Preserving Model Reduction of Low-Frequency Electromagnetic Problem Based on POD and DEIM
http://hdl.handle.net/10985/16570
Structure Preserving Model Reduction of Low-Frequency Electromagnetic Problem Based on POD and DEIM
MONTIER, Laurent; PIERQUIN, Antoine; HENNERON, Thomas; CLENET, Stéphane
The Proper Orthogonal Decomposition (POD) combined with the (Discrete) Empirical Interpolation Method (DEIM) can be used to reduce the computation time of the solution of a Finite Element (FE) model. However, it can lead to numerical instabilities. To increase the robustness, the POD_DEIM model must be constructed by preserving the structure of the full FE model. In this article, the structure preserving is applied for different potential formulations used to solve electromagnetic problems.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/165702017-01-01T00:00:00ZMONTIER, LaurentPIERQUIN, AntoineHENNERON, ThomasCLENET, StéphaneThe Proper Orthogonal Decomposition (POD) combined with the (Discrete) Empirical Interpolation Method (DEIM) can be used to reduce the computation time of the solution of a Finite Element (FE) model. However, it can lead to numerical instabilities. To increase the robustness, the POD_DEIM model must be constructed by preserving the structure of the full FE model. In this article, the structure preserving is applied for different potential formulations used to solve electromagnetic problems.Data-Driven Model Order Reduction for Magnetostatic Problem Coupled with Circuit Equations
http://hdl.handle.net/10985/12497
Data-Driven Model Order Reduction for Magnetostatic Problem Coupled with Circuit Equations
PIERQUIN, Antoine; HENNERON, Thomas; CLENET, Stéphane
Among the model order reduction techniques, the Proper Orthogonal Decomposition (POD) has shown its efficiency to solve magnetostatic and magneto-quasistatic problems in the time domain. However, the POD is intrusive in the sense that it requires the extraction of the matrix system of the full model to build the reduced model. To avoid this extraction, nonintrusive approaches like the Data Driven (DD) methods enable to approximate the reduced model without the access to the full matrix system. In this article, the DD-POD method is applied to build a low dimensional system to solve a magnetostatic problem coupled with electric circuit equations.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/124972017-01-01T00:00:00ZPIERQUIN, AntoineHENNERON, ThomasCLENET, StéphaneAmong the model order reduction techniques, the Proper Orthogonal Decomposition (POD) has shown its efficiency to solve magnetostatic and magneto-quasistatic problems in the time domain. However, the POD is intrusive in the sense that it requires the extraction of the matrix system of the full model to build the reduced model. To avoid this extraction, nonintrusive approaches like the Data Driven (DD) methods enable to approximate the reduced model without the access to the full matrix system. In this article, the DD-POD method is applied to build a low dimensional system to solve a magnetostatic problem coupled with electric circuit equations.