| Project/Area Number |
15540136
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Keio University |
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Principal Investigator |
NODERA Takashi Keio Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (50156212)
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| Co-Investigator(Kenkyū-buntansha) |
MAEJIMA Makoto Keio Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (90051846)
TANI Atsushi Keio Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (90118969)
TAMURA Yozo Keio Univ., Faculty of Sci.and Tech., Associate Professor, 理工学部, 助教授 (50171905)
SHIMOMURA Shun Keio Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (00154328)
OHNO Yoshio Keio Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (20051865)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | sparse matrix computation / QCD / shifted system of equation / parallel computation / GMRES / preconditioning / approximate inverse / minimal residual method / 行列計算 / シュールコンプリメント / 並列計算 / グリッドコンピューティング |
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| Research Abstract |
Quantum Chromo dynamics (QCD) is the quantum theory of working together with quarks and gluons. It should make clear the physics of strong force from low to high energies. The direct attack it is known to be the lattice approach. This theory is called to be Lattice QCD (LQCD).
One important example is simulations in Lattice QCD with Neuberger fermions. The most important problem in this research is to find an approximate solution to the large linear systems of equations. From parallel computational point of view, iterative Krylov solvers are admired for approximately solving such the large linear systems of equations. In addition to the design of the toolkit, we have presented our approach to make up the different combinations of Krylov space generation and its preconditioning along with the orthogonality condition imposed on the residual at each step give rise to the different algorithms.
Generally, Krylov subspace methods have to be used with preconditiong, The use of approximate inverses have become a good alternative to implicit preconditioners due to their parallel nature. The main application is developed for the subspace of matrices with a given sparsity pattern which constructed iteratively by augmenting the set of non-zero entries in each column. We are developed three types of parallel approximate inverse preconditioner as follows,
(i)Newton type, (ii)Minimal residual type, (iii)Sherman-Morrison type
The effectiveness of the above sparse preconditioners was also shown with some numerical experiments of other PDE problems.
Our present work will be continued to cover up more general numerical problems and their analysis.
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