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New multigrid method including elimination algorithm based on high‐order vector finite elements in three‐dimensional magnetostatic field analysis
Author(s) -
Hano Mitsuo,
Hotta Masashi
Publication year - 2009
Publication title -
electronics and communications in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.131
H-Index - 13
eISSN - 1942-9541
pISSN - 1942-9533
DOI - 10.1002/ecj.10228
Subject(s) - multigrid method , finite element method , mathematics , convergence (economics) , coefficient matrix , algorithm , field (mathematics) , matrix (chemical analysis) , gaussian elimination , gauss , computer science , mathematical analysis , partial differential equation , gaussian , physics , pure mathematics , eigenvalues and eigenvectors , materials science , quantum mechanics , economics , composite material , thermodynamics , economic growth
A new multigrid method based on high‐order vector finite elements is proposed in this paper. Low‐level discretizations in this method are obtained by using low‐order vector finite elements for the same mesh. The Gauss–Seidel method is used as a smoother, and a linear equation of lowest level is solved by the ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algorithm of constant term using a null space of the coefficient matrix is also described. In three‐dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the conventional ICCG method. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 92(1): 39–45, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ecj.10228