Difference between revisions of "Projecthp-MSFEMs"

From Wiki
Jump to: navigation, search
(Abstract)
Line 26: Line 26:
  
 
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 di�erent. The thickness of iron laminates is about 0.3mm
+
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
Line 32: Line 32:
 
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 �nite element methods (MSFEMs) for ECs in laminated iron
+
The development of multiscale finite element methods (MSFEMs) for ECs in laminated iron
has brought the simulation capabilities a major step forward. Nevertheless, MSFEMs su�er
+
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 di�culties are major challenges in
+
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 di�erent potential formulations, higher order
+
Adaptive MSFEMs facilitating MSFEMs with different potential formulations, higher order
MSFEMs, harmonic balance MSFEMs etc. are absolutely unique and novel. E�cient and
+
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-re�nement will be developed.
+
of Prager and Synge to allow both h- and p-refinement will be developed.
The simulation of one laminate often su�ces for electrical machines assuming common simpli
+
The simulation of one laminate often suffices for electrical machines assuming common simpli
�cations. To avoid expensive 3D FE simulations, completely new space splitting 2-D/1-D
+
fications. To avoid expensive 3D FE simulations, completely new space splitting 2-D/1-D
methods will be developed considering in particular the edge e�ect and Biot-Savart-�elds,
+
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 �elds are a very serious shortcoming of
+
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 �elds
+
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 di�erent
+
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 speci�c nature of MSFEMs of ECs will be provided to cope with large nonlinear systems
+
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 di�culty. Unique adaptive MSFEMs
+
to run such simulations on personal computers without any difficulty. Unique adaptive MSFEMs
will guarantee highly accurate and e�cient MSFEM solutions. Novel MSFEMs will
+
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

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.