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http://hdl.handle.net/10985/10555
Application of the PGD and DEIM to solve a 3D Non-Linear Magnetostatic Problem coupled with the Circuit Equations
HENNERON, Thomas; CLENET, Stéphane
Among the model order reduction techniques, the Proper Generalized Decomposition (PGD) has shown its efficiency to solve static and quasistatic problems in the time domain. However, the introduction of nonlinearity due to ferromagnetic materials for example has never been addressed. In this paper, the PGD technique combined with the Discrete Empirical Interpolation Method (DEIM) is applied to solve a non-linear problem in magnetostatic coupled with the circuit equations. To evaluate the reduction technique, the transient state of a three phase transformer at no load is studied using the full Finite Element model and the PGD_DEIM model.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/105552015-01-01T00:00:00ZHENNERON, ThomasCLENET, StéphaneAmong the model order reduction techniques, the Proper Generalized Decomposition (PGD) has shown its efficiency to solve static and quasistatic problems in the time domain. However, the introduction of nonlinearity due to ferromagnetic materials for example has never been addressed. In this paper, the PGD technique combined with the Discrete Empirical Interpolation Method (DEIM) is applied to solve a non-linear problem in magnetostatic coupled with the circuit equations. To evaluate the reduction technique, the transient state of a three phase transformer at no load is studied using the full Finite Element model and the PGD_DEIM model.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.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.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.Balanced Proper Orthogonal Decomposition Applied to Magnetoquasistatic Problems Through a Stabilization Methodology
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.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.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.