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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.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.Application of the Proper Generalized Decomposition to Solve MagnetoElectric Problem
http://hdl.handle.net/10985/12496
Application of the Proper Generalized Decomposition to Solve MagnetoElectric Problem
HENNERON, Thomas; CLENET, Stéphane
Among the model order reduction techniques, the Proper Generalized Decomposition (PGD) has shown its efficiency to solve a large number of engineering problems. In this article, the PGD approach is applied to solve a multi-physics problem based on a magnetoelectric device. A reduced model is developed to study the device in its environment based on an Offline/Online approach. In the Offline step, two specific simulations are performed in order to build a PGD reduced model. Then, we obtain a model very well fitted to study in the Online stage the influence of parameters like the frequency or the load. The reduced model of the device is coupled with an electric load (R-L) to illustrate the possibility offered by the PGD.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/124962017-01-01T00:00:00ZHENNERON, ThomasCLENET, StéphaneAmong the model order reduction techniques, the Proper Generalized Decomposition (PGD) has shown its efficiency to solve a large number of engineering problems. In this article, the PGD approach is applied to solve a multi-physics problem based on a magnetoelectric device. A reduced model is developed to study the device in its environment based on an Offline/Online approach. In the Offline step, two specific simulations are performed in order to build a PGD reduced model. Then, we obtain a model very well fitted to study in the Online stage the influence of parameters like the frequency or the load. The reduced model of the device is coupled with an electric load (R-L) to illustrate the possibility offered by the PGD.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.Proper Generalized Decomposition Applied on a Rotating Electrical Machine
http://hdl.handle.net/10985/12495
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.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/124952017-01-01T00:00:00ZMONTIER, 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.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.Proper Generalized Decomposition method applied to solve 3D Magneto Quasistatic Field Problems coupling with External Electric Circuits
http://hdl.handle.net/10985/9862
Proper Generalized Decomposition method applied to solve 3D Magneto Quasistatic Field Problems coupling with External Electric Circuits
HENNERON, Thomas; CLENET, Stéphane
In the domain of numerical computation, Proper Generalized Decomposition (PGD), which consists of approximating the solution by a truncated sum of separable functions, is more and more applied in mechanics and has shown its efficiency in terms of computation time and memory requirements. We propose to evaluate the PGD method in order to solve 3D quasi static field problems coupling with an external electric circuit. The numerical model, obtained from the PGD formulation, is used to study 3D examples. The results are compared to those obtained when solving the full original problem. It is shown in this paper that the computation time rate versus the number of time steps is very small compared to the one a classical time stepping method and can be very efficient to solve problems when small time steps are required.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/98622014-01-01T00:00:00ZHENNERON, ThomasCLENET, StéphaneIn the domain of numerical computation, Proper Generalized Decomposition (PGD), which consists of approximating the solution by a truncated sum of separable functions, is more and more applied in mechanics and has shown its efficiency in terms of computation time and memory requirements. We propose to evaluate the PGD method in order to solve 3D quasi static field problems coupling with an external electric circuit. The numerical model, obtained from the PGD formulation, is used to study 3D examples. The results are compared to those obtained when solving the full original problem. It is shown in this paper that the computation time rate versus the number of time steps is very small compared to the one a classical time stepping method and can be very efficient to solve problems when small time steps are required.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.