1. Domain Decomposition Algorithms for Parallel Solution of Magnetic Field Problems D ÁNIEL M ARCSA, M IKLÓS K UCZMANN Laboratory of Electromagnetic Field, Department of Automation „Széchenyi István“ University, H-9026, Egyetem tér 1, Győr, Hungary E-mail: marcsad@sze.hu 13th International Symposium Estonia, P ä rnu, January 14-19, 2013 SZÉCHENYI ISTVÁN UNIVERSITY HTTP://UNI.SZE.HU 15-3210-02 LABORATORY OF ELECTROMAGNTIC FIELDS SZÉCHENYI ISTVÁN UNIVERSITY HTTP://MAXWELL.SZE.HU

2. LABORATORY OF ELECTROMAGNTIC FIELDS SZÉCHENYI ISTVÁN UNIVERSITY HTTP://MAXWELL.SZE.HU The Idea of Domain Decomposition Divide the domain Ω into several sub-domains in which the unknown potentials could be calculated simultaneously. 13th International Symposium Estonia, Pärnu, January 14-19, 2013 D. Marcsa, M. Kuczmann

3. LABORATORY OF ELECTROMAGNTIC FIELDS SZÉCHENYI ISTVÁN UNIVERSITY HTTP://MAXWELL.SZE.HU FETI Method D. Marcsa, M. Kuczmann 13th International Symposium Estonia, Pärnu, January 14-19, 2013 Linear algebraic problem Interface problem Direct solver Modified CG Preconditioned Mod. CG

4. LABORATORY OF ELECTROMAGNTIC FIELDS SZÉCHENYI ISTVÁN UNIVERSITY HTTP://MAXWELL.SZE.HU Floating Subdomains D. Marcsa, M. Kuczmann Subdomains with Neumann boundary condition. Subdomains with Dirichlet boundary condition. 13th International Symposium Estonia, Pärnu, January 14-19, 2013

5. LABORATORY OF ELECTROMAGNTIC FIELDS SZÉCHENYI ISTVÁN UNIVERSITY HTTP://MAXWELL.SZE.HU Test Problems D. Marcsa, M. Kuczmann Single-phase shell type transformer Three-phase induction motor 13th International Symposium Estonia, Pärnu, January 14-19, 2013

6. LABORATORY OF ELECTROMAGNTIC FIELDS SZÉCHENYI ISTVÁN UNIVERSITY HTTP://MAXWELL.SZE.HU Transformer – 55333 DoF D. Marcsa, M. Kuczmann Comparison of sequential and parallel finite element program. No. of Int. N. MCG iter. PMGC iter. 28226553 40637978 50238872 63257695 747637193 811703135 896774138 13th International Symposium Estonia, Pärnu, January 14-19, 2013

7. LABORATORY OF ELECTROMAGNTIC FIELDS SZÉCHENYI ISTVÁN UNIVERSITY HTTP://MAXWELL.SZE.HU Induction Motor – 106828 DoF D. Marcsa, M. Kuczmann Comparison of domain decomposition methods for a larger problem. No. of Int. N. MGC iter. PMGC iter. 525679337 646887298 7941001494 9131182597 10661198541 13th International Symposium Estonia, Pärnu, January 14-19, 2013

8. LABORATORY OF ELECTROMAGNTIC FIELDS SZÉCHENYI ISTVÁN UNIVERSITY HTTP://MAXWELL.SZE.HU Transformer – 70555 DoF D. Marcsa, M. Kuczmann Comparison of domain decomposition methods for a problem with floating subdomain. No. of Int. N. PMGC iter. 777100 1067210 1056121 1177125 13th International Symposium Estonia, Pärnu, January 14-19, 2013

9. LABORATORY OF ELECTROMAGNTIC FIELDS SZÉCHENYI ISTVÁN UNIVERSITY HTTP://MAXWELL.SZE.HU Conclusion and Future Work D. Marcsa, M. Kuczmann The speedup achieved nearly 11- fold, 3-fold, and 2-fold speedup. Seems to be the direct solver is the fastest. However, if the problem contain floating subdomain the PMCG is best solver. Implemented the DP-FETI method, which does not use floating subdomain. Used the domain decomposition methods for „real life” electromagnetic problems. 13th International Symposium Estonia, Pärnu, January 14-19, 2013