Auto-Gauging of Vector Potential by Parallel Sparse Direct Solvers-Numerical Observations

When using magnetic vector potential (MVP)-based formulations for magnetostatic or eddy-current problems, either gauge conditions specifying the divergence of the MVP or tree gauging by eliminating redundant degrees of freedom of the MVP is usually imposed to ensure uniqueness of solutions. Explicit...

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Vydáno v:IEEE transactions on magnetics Ročník 55; číslo 6; s. 1 - 5
Hlavní autoři: Tang, Zuqi, Zhao, Yanpu, Ren, Zhuoxiang
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.06.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Témata:
Divergence
Eddy current
Eddy currents
Electromagnetism
Engineering Sciences
finite-element (FE) method
Formulations
Gaging
gauge
Iterative methods
Magnetic domains
Magnetic resonance imaging
magnetic vector potential (MVP)
Magnetic vector potentials
Magnetism
magnetostatic
Magnetostatics
Matrix methods
Null space
parallel sparse direct solver (PSDS)
Random access memory
Solvers
Sparse matrices
Symmetric matrices
ISSN:0018-9464, 1941-0069
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Popis
Shrnutí:When using magnetic vector potential (MVP)-based formulations for magnetostatic or eddy-current problems, either gauge conditions specifying the divergence of the MVP or tree gauging by eliminating redundant degrees of freedom of the MVP is usually imposed to ensure uniqueness of solutions. Explicit gauging of the MVP is not always necessary since classical iterative solvers can automatically and implicitly fix the gauge as long as the right-hand side vectors are consistent. Besides iterative solvers, implicit gauging is also observed when using state-of-the-art parallel sparse direct solvers (PSDSs), thanks to the built-in functions of handling null-spaces of either real symmetric positive semi-definite matrix systems or those complex symmetric systems from eddy-current problems. Both static and eddy-current examples are solved by PSDS to demonstrate results of local physical quantities or global quantities such as magnetic energy or joule losses. High-order edge/nodal elements are also considered in our numerical examples and it is observed that PSDS can also easily and correctly handle the delicate discrete null spaces.
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ISSN:0018-9464
1941-0069
DOI:10.1109/TMAG.2019.2892868