2006 Fiscal Year Final Research Report Summary
Fast Electromagnetic Mortar Finite Element Analyses with High Accuracy Based on Algebraic Multigrid Methods
| Project/Area Number |
17560255
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
電力工学・電気機器工学
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| Research Institution | Kyoto University |
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Principal Investigator |
SHIMASAKI Masaaki Kyoto University, Graduate School of Engineering, Professor, 工学研究科, 教授 (60026242)
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| Co-Investigator(Kenkyū-buntansha) |
MATSUO Tetsuji Graduate School of Engineering, Associate Professor, 工学研究科, 助教授 (20238976)
IWASHITA Takeshi Academic Center for Computing and Media Studies, Associate Professor, 助教授 (30324685)
MIFUNE Takeshi Graduate School of Engineering, Research Associate, 工学研究科, 助手 (20362460)
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| Project Period (FY) |
2005 – 2006
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| Keywords | Electromagnetic Analyses / Mortar Finite Element Methods / Algebraic Multigrid Methods / Motor Analyses / Sliding Mesh |
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| Research Abstract |
(1)Research on iterative methods for mortar finite element analyses
Two type formulations are selectable in mortar finite element analyses: one with Lagrange multipliers and the other with elimination of variables on the slave-side boundaries. We propose several new preconditioning techniques, which are based on the incomplete Cholesky decomposition, for linear equations arising from the both formulations. One of the proposed preconditioners applies the incomplete Cholesky decomposition to an approximate coefficient matrix. Numerical tests demonstrate that a combination of the variable elimination and approximation of the matrix is promising from a viewpoint of the elapsed time to solve the equations.
(2)Mortar finite element analyses using algebraic multigrid methods In a preliminary study, we develop algebraic multigrid (AMG) methods, which are efficient preconditioners for sparse matrices arising from the finite edge-and nodal element analyses.
For the mortar finite element analyses, w
… More
e propose an effective iterative solver preconditioned by the AMG method. Whereas the variable elimination formulation leads to a dense coefficient matrix, the AMG preconditioner is efficiently applied to a sparse matrix, which is an approximation of the original dense matrix. Numerical tests demonstrate an excellent performance of the proposed solver, compared with conventional solvers. The proposed solver can be applied to problems with anti-periodic boundary conditions.
(3)Fast nonlinear magnetic analyses using algebraic multigrid methods
We present a fast nonlinear finite element analysis with the magnetic scalar potential as unknowns. In the Newton-Raphson (NR) iterations, the linear equations are solved by an AMG preconditioned conjugate gradient (CG) solver. The line-search method is applied to improve the convergence of NR iterations. Numerical results show that the AMG-CG solver is efficient for the nonlinear analysis of a benchmark model. Moreover, a considerable speed-up is achieved by relaxing the convergence criterion of the CG iterations. Less
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