Similarities Between Implicit Correction Multigrid Method and A-phi Formulation in Electromagnetic Field Analysis

This paper proposes an implicit error correction method that corresponds to the explicit error correction methods, such as Hiptmair's hybrid smoother and the conventional multigrid method. The A-phi method can be seen as the implicit error correction method corresponding to the hybrid smoother....

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Bibliographic Details
Published in:IEEE transactions on magnetics 2008-06, Vol.44 (6), p.946-949
Main Authors: Iwashita, T., Mifune, T., Shimasaki, M.
Format: Article
Language:English
Subjects:
A-phi method
Analogies
Convergence
Convergence of numerical methods
Cross-disciplinary physics: materials science
rheology
Electromagnetic analysis
Electromagnetic fields
Electromagnetism
Equations
Error correction
Error correction & detection
Exact sciences and technology
hybrid smoother
implicit error correction
iterative method
Iterative methods
Kernel
Linear systems
Magnetism
Materials science
Mathematical models
multigrid method
Multigrid methods
Other topics in materials science
Physics
Solvers
Studies
Testing
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Summary:This paper proposes an implicit error correction method that corresponds to the explicit error correction methods, such as Hiptmair's hybrid smoother and the conventional multigrid method. The A-phi method can be seen as the implicit error correction method corresponding to the hybrid smoother. Numerical tests confirm that the A-phi method produces a similar correction effect on the error belonging to the kernel of the discrete curl operator as that of the hybrid smoother. Furthermore, this paper introduces an implicit correction multigrid method, which is the implicit error correction version of the conventional multigrid method. In this method, linear systems on all levels in a multigrid method are combined into a large linear system. This linear system is solved by an iterative solver, and any preconditioning techniques can be used. Numerical tests show that the proposed method involves coarse grid correction effects and achieves a convergence rate independent of the grid-size, thus confirming the effectiveness of the implicit error correction method.
ISSN:0018-9464
1941-0069
DOI:10.1109/TMAG.2007.915076