IETI-DP Solvers in Simulation and Optimization of Electrical Machines

DI Rainer Schneckenleitner

June 18, 2019, 1:45 p.m. S2 416-1

Highly efficient electric motors will play a decisive role in future e-mobility. In [2], multipatch continuous
Galerkin Isogeometric Analysis (IgA) discretization was used for the simulation and shape optimization
of electrical machines in a fixed position. We mention that IgA allows an exact representation of the
geometry of an electric motor. In order to get fast simulation and optimization results, the large-scale
systems of algebraic equations arising from the IgA discretization of underlying partial differential equations
were solved by Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods. This
class of domain decomposition (DD) methods is naturally related to the multipatch representation of the
computational domain, and provides an excellent framework for the parallelization of the DD solvers.
In order to handle moving interfaces, and, in particular, the rotation of an electrical machine, we use
discontinuous Galerkin (dG) IgA discretization, at least, along the moving interfaces. Furthermore, we
generalize the dG IETI-DP solver introduced in [1] to the the case of non-conformely matching patches.
In particular, we cannot use the patch vertices as primal unknows. Instead of that, we use only edge
averages. The numerical results confirme the efficiency of the dG IgA discretization and dG IETI-DP
solution techniques.
[1] Hofer, C. and Langer, U. Dual-Primal Isogeometric Tearing and Interconnecting solvers for multipatch
dG-IgA equations. Comput. Methods Appl. Mech. Engrg. (2017)316:2–21.
[2] Gangl, P., Langer, U., Mantzaflaris, A. and Schneckenleitner, R. Isogeometric Simulation and
Shape Optimization with Applications to Electrical Machines. arXiv:1809.03377 (2018), accepted
for publication in the SCEE 2018 proceedings.