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http://hdl.handle.net/10985/11755
Balanced Proper Orthogonal Decomposition Applied to Magnetoquasistatic Problems Through a Stabilization Methodology
MONTIER, Laurent; HENNERON, Thomas; GOURSAUD, Benjamin; CLENET, Stéphane
Model Order Reduction (MOR) methods are applied in different areas of physics in order to reduce the computational time of large scale systems. It has been an active field of research for many years, in mechanics especially, but it is quite recent for magnetoquasistatic problems. Although the most famous method, the Proper Orthogonal Decomposition (POD) has been applied for modelling many electromagnetic devices, this method can lack accuracy for low order magnitude output quantities, like flux associated with a probe in regions where the field is low. However, the Balanced Proper Orthogonal Decomposition (BPOD) is a MOR method which takes into account these output quantities in its reduced model to render them accurately. Even if the BPOD may lead to unstable reduced systems, this can be overcome by a stabilization procedure. Therefore, the POD and stabilized BPOD will be compared on a 3D linear magnetoquasistatic field problem.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/117552017-01-01T00:00:00ZMONTIER, LaurentHENNERON, ThomasGOURSAUD, BenjaminCLENET, StéphaneModel Order Reduction (MOR) methods are applied in different areas of physics in order to reduce the computational time of large scale systems. It has been an active field of research for many years, in mechanics especially, but it is quite recent for magnetoquasistatic problems. Although the most famous method, the Proper Orthogonal Decomposition (POD) has been applied for modelling many electromagnetic devices, this method can lack accuracy for low order magnitude output quantities, like flux associated with a probe in regions where the field is low. However, the Balanced Proper Orthogonal Decomposition (BPOD) is a MOR method which takes into account these output quantities in its reduced model to render them accurately. Even if the BPOD may lead to unstable reduced systems, this can be overcome by a stabilization procedure. Therefore, the POD and stabilized BPOD will be compared on a 3D linear magnetoquasistatic field problem.Error Estimation for Model Order Reduction of Finite Element Parametric Problems
http://hdl.handle.net/10985/11034
Error Estimation for Model Order Reduction of Finite Element Parametric Problems
CLENET, Stéphane; HENNERON, Thomas
To solve a parametric model in computational electromagnetics, the Finite Element method is often used. To reduce the computational time and the memory requirement, the Finite Element method can be combined with Model Order Reduction Technic like the Proper Orthogonal Decomposition (POD) and the (Discrete) Empirical Interpolation ((D)EI) Methods. These three numerical methods introduce errors of discretisation, reduction and interpolation respectively. The solution of the parametric model will be efficient if the three errors are of the same order and so they need to be evaluated and compared. In this paper, we propose an aposteriori error estimator based on the verification of the constitutive law which estimates the three different errors. An example of application in magnetostatics with 11 parameters is treated where it is shown how the error estimator can be used to control and to improve the accuracy of the solution of the reduced model.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/110342016-01-01T00:00:00ZCLENET, StéphaneHENNERON, ThomasTo solve a parametric model in computational electromagnetics, the Finite Element method is often used. To reduce the computational time and the memory requirement, the Finite Element method can be combined with Model Order Reduction Technic like the Proper Orthogonal Decomposition (POD) and the (Discrete) Empirical Interpolation ((D)EI) Methods. These three numerical methods introduce errors of discretisation, reduction and interpolation respectively. The solution of the parametric model will be efficient if the three errors are of the same order and so they need to be evaluated and compared. In this paper, we propose an aposteriori error estimator based on the verification of the constitutive law which estimates the three different errors. An example of application in magnetostatics with 11 parameters is treated where it is shown how the error estimator can be used to control and to improve the accuracy of the solution of the reduced model.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.Error estimation of a proper orthogonal decomposition reduced model of a permanent magnet synchronous machine
http://hdl.handle.net/10985/9264
Error estimation of a proper orthogonal decomposition reduced model of a permanent magnet synchronous machine
HENNERON, Thomas; MAC, Hung; CLENET, Stéphane
Model order reduction methods, like the proper orthogonal decomposition (POD), enable to reduce dramatically the size of a finite element (FE) model. The price to pay is a loss of accuracy compared with the original FE model that should be of course controlled. In this study, the authors apply an error estimator based on the verification of the constitutive relationship to compare the reduced model accuracy with the full model accuracy when POD is applied. This estimator is tested on an example of a permanent magnet synchronous machine.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/92642015-01-01T00:00:00ZHENNERON, ThomasMAC, HungCLENET, StéphaneModel order reduction methods, like the proper orthogonal decomposition (POD), enable to reduce dramatically the size of a finite element (FE) model. The price to pay is a loss of accuracy compared with the original FE model that should be of course controlled. In this study, the authors apply an error estimator based on the verification of the constitutive relationship to compare the reduced model accuracy with the full model accuracy when POD is applied. This estimator is tested on an example of a permanent magnet synchronous machine.Model Order Reduction of Non-Linear Magnetostatic Problems Based on POD and DEI Methods
http://hdl.handle.net/10985/7816
Model Order Reduction of Non-Linear Magnetostatic Problems Based on POD and DEI Methods
HENNERON, Thomas; CLENET, Stéphane
In the domain of numerical computation, Model Order Reduction approaches are more and more frequently applied in mechanics and have shown their efficiency in terms of reduction of computation time and memory storage requirements. One of these approaches, the Proper Orthogonal Decomposition (POD), can be very efficient in solving linear problems but encounters limitations in the non-linear case. In this paper, the Discret Empirical Interpolation Method coupled with the POD method is presented. This is an interesting alternative to reduce large-scale systems deriving from the discretization of non-linear magnetostatic problems coupled with an external electrical circuit.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/78162014-01-01T00:00:00ZHENNERON, ThomasCLENET, StéphaneIn the domain of numerical computation, Model Order Reduction approaches are more and more frequently applied in mechanics and have shown their efficiency in terms of reduction of computation time and memory storage requirements. One of these approaches, the Proper Orthogonal Decomposition (POD), can be very efficient in solving linear problems but encounters limitations in the non-linear case. In this paper, the Discret Empirical Interpolation Method coupled with the POD method is presented. This is an interesting alternative to reduce large-scale systems deriving from the discretization of non-linear magnetostatic problems coupled with an external electrical circuit.Non Linear Proper Generalized Decomposition method applied to the magnetic simulation of a SMC microstructure
http://hdl.handle.net/10985/7815
Non Linear Proper Generalized Decomposition method applied to the magnetic simulation of a SMC microstructure
HENNERON, Thomas; BENABOU, Abdelkader; CLENET, Stéphane
Improvement of the magnetic performances of Soft Magnetic Composites (SMC) materials requires to link the microstructures to the macroscopic magnetic behavior law. This can be achieved with the FE method using the geometry reconstruction from images of the microstructure. Nevertheless, it can lead to large computational times. In that context, the Proper Generalized Decomposition (PGD), that is an approximation method originally developed in mechanics, and based on a finite sum of separable functions, can be of interest in our case. In this work, we propose to apply the PGD method to the SMC microstructure magnetic simulation. A non-linear magnetostatic problem with the scalar potential formulation is then solved.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/78152012-01-01T00:00:00ZHENNERON, ThomasBENABOU, AbdelkaderCLENET, StéphaneImprovement of the magnetic performances of Soft Magnetic Composites (SMC) materials requires to link the microstructures to the macroscopic magnetic behavior law. This can be achieved with the FE method using the geometry reconstruction from images of the microstructure. Nevertheless, it can lead to large computational times. In that context, the Proper Generalized Decomposition (PGD), that is an approximation method originally developed in mechanics, and based on a finite sum of separable functions, can be of interest in our case. In this work, we propose to apply the PGD method to the SMC microstructure magnetic simulation. A non-linear magnetostatic problem with the scalar potential formulation is then solved.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.Comparison 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.Proper Generalized Decomposition Applied on a Rotating Electrical Machine
http://hdl.handle.net/10985/12734
Proper Generalized Decomposition Applied on a Rotating Electrical Machine
MONTIER, Laurent; HENNERON, Thomas; CLENET, Stéphane; GOURSAUD, Benjamin
The Proper Generalized Decomposition (PGD) is a model order reduction method which allows to reduce the computational time of a numerical problem by seeking for a separated representation of the solution. The PGD has been already applied to study an electrical machine but at standstill without accounting the motion of the rotor. In this paper, we propose a method to account for the rotation in the PGD approach in order to build an efficient metamodel of an electrical machine. Then, the machine metamodel will be coupled to its electrical and mechanical environment in order to obtain accurate results with an acceptable computational time on a full simulation.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/127342018-01-01T00:00:00ZMONTIER, LaurentHENNERON, ThomasCLENET, StéphaneGOURSAUD, BenjaminThe Proper Generalized Decomposition (PGD) is a model order reduction method which allows to reduce the computational time of a numerical problem by seeking for a separated representation of the solution. The PGD has been already applied to study an electrical machine but at standstill without accounting the motion of the rotor. In this paper, we propose a method to account for the rotation in the PGD approach in order to build an efficient metamodel of an electrical machine. Then, the machine metamodel will be coupled to its electrical and mechanical environment in order to obtain accurate results with an acceptable computational time on a full simulation.Data-Driven Model Order Reduction for Magnetostatic Problem Coupled with Circuit Equations
http://hdl.handle.net/10985/12997
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.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/129972018-01-01T00:00:00ZPIERQUIN, 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.