TY - JOUR
T1 - Inverse Scheme to Locally Determine Nonlinear Magnetic Material Properties
T2 - Numerical Case Study
AU - Kaltenbacher, Manfred
AU - Gschwentner, Andreas
AU - Kaltenbacher, Barbara
AU - Ulbrich, Stefan
AU - Reinbacher-Köstinger, Alice
N1 - Publisher Copyright:
© 2024 by the authors.
PY - 2024/5
Y1 - 2024/5
N2 - We are interested in the determination of the local nonlinear magnetic material behaviour in electrical steel sheets due to cutting and punching effects. For this purpose, the inverse problem has to be solved, where the objective function, which penalises the difference between the measured and the simulated magnetic flux density, has to be minimised under a constraint defined according to the corresponding partial differential equation model. We use the adjoint method to efficiently obtain the gradients of the objective function with respect to the material parameters. The optimisation algorithm is low-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS), the forward and adjoint formulations are solved using the finite element (FE) method and the ill-posedness is handled via Tikhonov regularisation, in combination with the discrepancy principle. Realistic numerical case studies show promising results.
AB - We are interested in the determination of the local nonlinear magnetic material behaviour in electrical steel sheets due to cutting and punching effects. For this purpose, the inverse problem has to be solved, where the objective function, which penalises the difference between the measured and the simulated magnetic flux density, has to be minimised under a constraint defined according to the corresponding partial differential equation model. We use the adjoint method to efficiently obtain the gradients of the objective function with respect to the material parameters. The optimisation algorithm is low-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS), the forward and adjoint formulations are solved using the finite element (FE) method and the ill-posedness is handled via Tikhonov regularisation, in combination with the discrepancy principle. Realistic numerical case studies show promising results.
KW - adjoint method
KW - determination of locally nonlinear magnetic material behaviour
KW - inverse problems
UR - http://www.scopus.com/inward/record.url?scp=85194043117&partnerID=8YFLogxK
U2 - 10.3390/math12101586
DO - 10.3390/math12101586
M3 - Article
AN - SCOPUS:85194043117
SN - 2227-7390
VL - 12
JO - Mathematics
JF - Mathematics
IS - 10
M1 - 1586
ER -