1993 Fiscal Year Final Research Report Summary
Algorithms for Large Scale Linear Systems in the Numerical Simulation
| Project/Area Number |
04640209
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tsukuba |
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Principal Investigator |
NATORI Makoto Inst.Info.Sci., Univ.of Tsukuba, Professor, 電子・情報工学系, 教授 (70013745)
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| Co-Investigator(Kenkyū-buntansha) |
IMAI Hitoshi Fac.Eng., Univ.of Tokushima, Assoc.Prof., 工学部, 助教授 (80203298)
SAKURAI Tetsuya Inst.Info.Sci., Univ.of Tsukuba, Assis.Prof., 電子・情報工学系, 講師 (60187086)
KITAGAWA Takashi Inst.Info.Sci., Univ.of Tsukuba, Assoc.Prof., 電子・情報工学系, 助教授 (60153095)
INAGAKI Toshiyuki Inst.Info.Sci., Univ.of Tsukuba, Assoc.Prof., 電子・情報工学系, 助教授 (60134219)
IKEBE Yasuhiko Inst.Info.Sci., Univ.of Tsukuba, Professor, 電子・情報工学系, 教授 (10114034)
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| Project Period (FY) |
1992 – 1993
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| Keywords | Large sparse matrix / Preconditioned CG method / Parallel algorithm / Matrix eigenvalue problem / Lanczos algorithm / III - posed problem / Free boundary problem / Natural convection |
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| Research Abstract |
In this research, algorithms to solve large scale linear systems appeared in the numerical simulation were investigated.
(1)We investigated preconditioned conjugate gradient methods to solve large scale linear systems of equations. Especially, We considered BiCGSTAB method which is known to be stable for asymmetric matrics. We developed a new preconditioner which enables parallel processing.
(2)We investigated Lanczos algorithm to compute eigenvalus of large sparse matrices. Especially, we concidered the block Lanczos algorithm for matrices which have degenerate eigenvalues. We developed a new reorthoganalization mehod for the block Lanczos algorithm.
(3)We investigated regularization methods for ill - posed problems. We developed new algorithms to estimate the value of the optimal regularization parameters.
(4)We carryed out the numerical simulations of solidification problems with change of valume and natural convection problems with a free surface.
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