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Domain Decomposition Algorithms for Parallel Solution of
Magnetic Field Problems
DÁNIEL MARCSA, MIKLÓS KUCZMANN
Laboratory of Electromagnetic Field, Department of Automation„Széchenyi István“ University, H-9026, Egyetem tér 1, Győr, Hungary
E-mail: [email protected]
13th International Symposium Estonia, Pärnu, January 14-19, 2013
SZÉCHENYI ISTVÁN UNIVERSITYHTTP://UNI.SZE.HU15-3210-02
LABORATORY OF ELECTROMAGNTIC FIELDSSZÉCHENYI ISTVÁN UNIVERSITY
HTTP://MAXWELL.SZE.HU
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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.
Divide the domain Ω into several sub-domains in which the unknown potentials could be calculated simultaneously.
13th International SymposiumEstonia, Pärnu, January 14-19, 2013D. Marcsa, M.
Kuczmann
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LABORATORY OF ELECTROMAGNTIC FIELDS
SZÉCHENYI ISTVÁN UNIVERSITY
HTTP://MAXWELL.SZE.HU
FETI Method
D. Marcsa, M. Kuczmann
SN
jjj
Tjjjj
1
0xB
λBbxK
bKx
0λBbR
αRλBbKx
TTjjj
jjTjjjj
13th International SymposiumEstonia, Pärnu, January 14-19, 2013
Linear algebraic problem
e
d
α
λ
0G
GFTI
II
Interface problemInterface problem
Direct solver Modified CG
Preconditioned
Mod. CG
edFGGFGα
αGdFλ
ITIII
TI
II
1
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LABORATORY OF ELECTROMAGNTIC FIELDS
SZÉCHENYI ISTVÁN UNIVERSITY
HTTP://MAXWELL.SZE.HU
Floating Subdomains
D. Marcsa, M. Kuczmann
D
N
D
D
Subdomainswith Neumann
boundary condition.
Subdomainswith Dirichlet
boundary condition.
13th International SymposiumEstonia, Pärnu, January 14-19, 2013
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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 SymposiumEstonia, Pärnu, January 14-19, 2013
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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.
MCGiter.
PMGC
iter.
282 265 53
406 379 78
502 388 72
632 576 95
747 637 193
811 703 135
896 774 138
13th International SymposiumEstonia, Pärnu, January 14-19, 2013
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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.
MGCiter.
PMGC
iter.
525 679 337
646 887 298
794 1001 494
913 1182 597
1066 1198 541
13th International SymposiumEstonia, Pärnu, January 14-19, 2013
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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.
777 100
1067 210
1056 121
1177 125
13th International SymposiumEstonia, Pärnu, January 14-19, 2013
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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 SymposiumEstonia, Pärnu, January 14-19, 2013
