2005 Fiscal Year Final Research Report Summary
Finite element analysis for 3-dimensional large scale problem by using domain decomposition methods
| Project/Area Number |
15360044
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | KYUSHU UNIVERSITY |
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Principal Investigator |
KANAYAMA Hiroshi KYUSHU UNIVERSITY, Faculty of Engineering, Professor, 大学院・工学研究院, 教授 (90294884)
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| Co-Investigator(Kenkyū-buntansha) |
FUJINO Seiji KYUSHU UNIVERSITY, Computing and Communications Center, Professor, 情報基盤センター, 教授 (40264965)
SUZUKI Atsushi KYUSHU UNIVERSITY, Faculty of Mathematics, Research Associate, 大学院・数理学研究院, 助手 (60284155)
TAGAMI Daisuke KYUSHU UNIVERSITY, Faculty of Engineering, Research Associate, 大学院・工学研究院, 助手 (40315122)
OGINO Masao KYUSHU UNIVERSITY, Faculty of Engineering, Research Associate, 大学院・工学研究院, 助手 (00380593)
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| Project Period (FY) |
2003 – 2005
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| Keywords | domain decomposition method / large scale problem / eddy current problem / thermal convection problem / Stokes equation / iterative solver / balancing preconditioner / parallel computation |
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| Research Abstract |
A.Numerical computations of large scale magnetic problems by finite element method:
First, we have developed computational codes for time-harmonic eddy current problems and nonlinear magnetostatic problems. To make the codes efficient, then we have considered the reduction of their computational costs, and the enhancement of applicable problems, for example, a permanent magnet or a moving obstacle.
B.Numerical solver for linear systems with symmetric coefficient matrices:
We have considered the convergence of MRTR method based on the minimization of residuals. Moreover, we have developed several precondisioners, which come from robust incomplete Cholesky factorization, and have shown their efficiency by appling to some real problems.
C.Application of a substracturing method to discretized Stokes equations:
We have established a coarse space of a balancing precondisioner for applying to discretized Stokes equations.
D.Error estimates of finite element methods for thermal convection problems:
We have established error estimates of a class of finite element methods for thermal convection problems with variable coefficients.
E.Realization of highly efficient BDD methods for large scale structural analysis:
We have developed incomplete BDD methods, improved its parallel efficiency, and realized nonstationary structural analysis with about 10 million DOF problems.
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