1988 Fiscal Year Final Research Report Summary
Research in Numerical Analysis of Free Boundary Problems
| Project/Area Number |
62540141
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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 Institute of Information Sciences and Electronics, University of Tsukuba, 電子情報工学系, 教授 (70013745)
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| Co-Investigator(Kenkyū-buntansha) |
IMAI Hitoshi Institute of Information Sciences and Electronics, University of Tsukuba, 電子情報工学系, 助手 (80203298)
INAGAKI Toshiyuki Institute of Information Sciences and Electronics, University of Tsukuba, 電子情報工学系, 助教授 (60134219)
OYANAGI Yoshio Institute of Information Sciences and Electronics, University of Tsukuba, 電子情報工学系, 教授 (60011673)
IKEBE Yasuhiko Institute of Information Sciences and Electronics, University of Tsukuba, 電子情報工学系, 教授 (10114034)
MORI Masatake Institute of Information Sciences and Electronics, University of Tsukuba, 電子情報工学系, 教授 (20010936)
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| Project Period (FY) |
1987 – 1988
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| Keywords | partial differential equation / free boundary problem / integrated penalty method / BEM / FEM / large sparse matrix / preconditioned conjugate gradient method / super-computer / 平衡プラズマ |
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| Research Abstract |
In this research, numerical methods to solve free boundary problems for partial differential equations were invastigated. The finite difference method combined with the integrated penalty method proposed by Kawarada and Natori, the boundary element method(BEM) and the finite element method(FEM) are used. A sharp interface problem arising in the flow of two immiscible fluids, slag and moltem metal, in a blast furnace was formulated usign a two and three dimensional model. For two dimensional case, the BEM and the FEM were compared. It turned out that the CPU time by the FEM was about half of that by the BEM. The ICCG method for the present sparse symmetric matrix equation plays a significant role in reducing the CPU time.
A free boundary problem for the shape of the two dimensional equilibrium plasma in the vessel was studied. It was munerically shown that asymmetric one-conponent plasmas exist in the vessel which has a symmetric cross section.
Numerical methods to solve large sparse system of linear equations were investigeted. Especially the preconditioned conjugate gradient method(PCG, ICCG) and the related methods were studied.
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