| Project/Area Number |
26520204
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 特設分野 |
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| Research Field |
Mathematical Sciences in Search of New Cooperation
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| Research Institution | Yamagata University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
齋藤 歩 山形大学, 大学院理工学研究科, 准教授 (20400533)
三浦 毅 新潟大学, 自然科学系, 教授 (90333989)
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| Project Period (FY) |
2014-07-18 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | メッシュレス法 / Krylov空間法 / 形状関数 / 拘束条件付き連立1次方程式 / 拘束条件付き連立１次方程式 / Krylov部分空間法 / 数値解析 / シミュレーション工学 |
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| Outline of Final Research Achievements |
If the elliptic boundary-value problem is discretized with the meshless approaches such as the EFG and the X-EFG, a special type of linear system is obtained. However, when the Krylov space method is applied to the resulting system, its convergence property is remarkably degraded with an increase in the number of constraints.
For the purpose of suppressing degradation of the convergence property, projector matrices onto the image space of the constraint matrix and its orthogonal complement are defined and, by using the projector matrices, the Lagrange multipliers are completely eliminated from the linear system. Moreover, the resulting linear system is numerically solved with the Krylov space method. As a result, it is found that, even if the number of constraints is increased, the convergence property of the linear-system solver will not be degraded at all. Hence, the proposed method can be a powerful tool for solving a linear system obtained by the meshless approaches.
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