# Difference between revisions of "Projecthp-MSFEMs"

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The iron core of electrical devices is laminated to reduce the eddy current (EC) losses. The | The iron core of electrical devices is laminated to reduce the eddy current (EC) losses. The | ||

− | geometric dimensions are extremely | + | geometric dimensions are extremely different. The thickness of iron laminates is about 0.3mm |

and separated by quite small air gaps. On the other hand, the overall dimensions of the core | and separated by quite small air gaps. On the other hand, the overall dimensions of the core | ||

are in the meter range consisting of up to several thousands of laminates. Finite element | are in the meter range consisting of up to several thousands of laminates. Finite element | ||

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of each laminate by FEs leads to an extremely large nonlinear system of equations, well above | of each laminate by FEs leads to an extremely large nonlinear system of equations, well above | ||

hundreds of millions, which cannot reasonably be solved with present computer capacities. | hundreds of millions, which cannot reasonably be solved with present computer capacities. | ||

− | The development of multiscale | + | The development of multiscale finite element methods (MSFEMs) for ECs in laminated iron |

− | has brought the simulation capabilities a major step forward. Nevertheless, MSFEMs | + | has brought the simulation capabilities a major step forward. Nevertheless, MSFEMs suffer |

from various shortcomings and the computational costs are still too high. There is no error | from various shortcomings and the computational costs are still too high. There is no error | ||

estimator for MSFEMs which is a big problem to trust in MSFEM solutions. MSFEMs | estimator for MSFEMs which is a big problem to trust in MSFEM solutions. MSFEMs | ||

− | in 3D are severely restricted to simple problems. These | + | in 3D are severely restricted to simple problems. These difficulties are major challenges in |

computational electromagnetics. Completely new methods will be developed to achieve the | computational electromagnetics. Completely new methods will be developed to achieve the | ||

breakthrough of MSFEMs. | breakthrough of MSFEMs. | ||

− | Adaptive MSFEMs facilitating MSFEMs with | + | Adaptive MSFEMs facilitating MSFEMs with different potential formulations, higher order |

− | MSFEMs, harmonic balance MSFEMs etc. are absolutely unique and novel. | + | MSFEMs, harmonic balance MSFEMs etc. are absolutely unique and novel. Efficient and |

reliable equilibrated local error estimators with a computable constant and based on the theorem | reliable equilibrated local error estimators with a computable constant and based on the theorem | ||

− | of Prager and Synge to allow both h- and p- | + | of Prager and Synge to allow both h- and p-refinement will be developed. |

− | The simulation of one laminate often | + | The simulation of one laminate often suffices for electrical machines assuming common simpli |

− | + | fications. To avoid expensive 3D FE simulations, completely new space splitting 2-D/1-D | |

− | methods will be developed considering in particular the edge | + | methods will be developed considering in particular the edge effect and Biot-Savart-fields, |

leading to a major reduction of computational costs. | leading to a major reduction of computational costs. | ||

− | The missing models for interfaces with large stray | + | The missing models for interfaces with large stray fields are a very serious shortcoming of |

− | MSFEMs in 3D. Feasible solutions in 3D are of exceptional importance, because stray | + | MSFEMs in 3D. Feasible solutions in 3D are of exceptional importance, because stray fields |

are present in almost all electrical devices. Current MSFEM approaches vanish in air which | are present in almost all electrical devices. Current MSFEM approaches vanish in air which | ||

represents a serious problem. Thus, radically new approaches have to be found. | represents a serious problem. Thus, radically new approaches have to be found. | ||

− | Novel nonlinear model order reduction (MOR) schemes have to be developed for | + | Novel nonlinear model order reduction (MOR) schemes have to be developed for different |

MSFEMs to achieve tremendous savings in computational costs. MOR schemes exploiting | MSFEMs to achieve tremendous savings in computational costs. MOR schemes exploiting | ||

− | the | + | the specific nature of MSFEMs of ECs will be provided to cope with large nonlinear systems |

of equations. | of equations. | ||

The aims of the project are a strong reduction of the high computational costs of MSFEMs | The aims of the project are a strong reduction of the high computational costs of MSFEMs | ||

− | to run such simulations on personal computers without any | + | to run such simulations on personal computers without any difficulty. Unique adaptive MSFEMs |

− | will guarantee highly accurate and | + | will guarantee highly accurate and efficient MSFEM solutions. Novel MSFEMs will |

solve the still existing shortcomings in 3D. | solve the still existing shortcomings in 3D. | ||

The project will be carried out by the applicant and the doctoral candidate. | The project will be carried out by the applicant and the doctoral candidate. |

## Revision as of 11:53, 12 November 2018

#### Project Manager

Institute for Analysis and Scientific Computing

Wiedner Hauptstrasse 8-10

A-1040 Vienna, Austria

Tel: +43 1 58801 10116

Email: karl.hollaus@tuwien.ac.at

#### Project Members

- Univ.Prof. Dr. Joachim Schöberl
- Dipl.-Ing. Markus Schöbinger (Ph.D. student)
- Valentin Hanser (Master student)

#### Open Positions

There are currently no vacant positions.

#### Funding

Fonds zur Förderung der wissenschaftlichen Forschung FWF

Grant number: P 31926

Funding periode: from November 1, 2018 to October 31, 2021

#### Abstract

The iron core of electrical devices is laminated to reduce the eddy current (EC) losses. The geometric dimensions are extremely different. The thickness of iron laminates is about 0.3mm and separated by quite small air gaps. On the other hand, the overall dimensions of the core are in the meter range consisting of up to several thousands of laminates. Finite element (FE) simulations are indispensable for the optimal design of the devices. However, modeling of each laminate by FEs leads to an extremely large nonlinear system of equations, well above hundreds of millions, which cannot reasonably be solved with present computer capacities. The development of multiscale finite element methods (MSFEMs) for ECs in laminated iron has brought the simulation capabilities a major step forward. Nevertheless, MSFEMs suffer from various shortcomings and the computational costs are still too high. There is no error estimator for MSFEMs which is a big problem to trust in MSFEM solutions. MSFEMs in 3D are severely restricted to simple problems. These difficulties are major challenges in computational electromagnetics. Completely new methods will be developed to achieve the breakthrough of MSFEMs. Adaptive MSFEMs facilitating MSFEMs with different potential formulations, higher order MSFEMs, harmonic balance MSFEMs etc. are absolutely unique and novel. Efficient and reliable equilibrated local error estimators with a computable constant and based on the theorem of Prager and Synge to allow both h- and p-refinement will be developed. The simulation of one laminate often suffices for electrical machines assuming common simpli fications. To avoid expensive 3D FE simulations, completely new space splitting 2-D/1-D methods will be developed considering in particular the edge effect and Biot-Savart-fields, leading to a major reduction of computational costs. The missing models for interfaces with large stray fields are a very serious shortcoming of MSFEMs in 3D. Feasible solutions in 3D are of exceptional importance, because stray fields are present in almost all electrical devices. Current MSFEM approaches vanish in air which represents a serious problem. Thus, radically new approaches have to be found. Novel nonlinear model order reduction (MOR) schemes have to be developed for different MSFEMs to achieve tremendous savings in computational costs. MOR schemes exploiting the specific nature of MSFEMs of ECs will be provided to cope with large nonlinear systems of equations. The aims of the project are a strong reduction of the high computational costs of MSFEMs to run such simulations on personal computers without any difficulty. Unique adaptive MSFEMs will guarantee highly accurate and efficient MSFEM solutions. Novel MSFEMs will solve the still existing shortcomings in 3D. The project will be carried out by the applicant and the doctoral candidate.

#### Software

Finite element package ngsolve for electromagnetic problems.