| Project/Area Number |
17K18738
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| Research Category |
Grant-in-Aid for Challenging Research (Exploratory)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Analysis, Applied mathematics, and related fields
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| Research Institution | Ehime University |
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Principal Investigator |
Tsuchiya Takuya 愛媛大学, 理工学研究科(理学系), 教授 (00163832)
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| Project Period (FY) |
2017-06-30 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2017: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 有限要素法 / 関数補間 / 三角形分割 / Crouzeix--Raviart補間 / Raviert--Thomas補間 / 誤差解析 / chunkiness parameter |
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| Outline of Final Research Achievements |
Numerical simulation is one of the most important technologies for the modern civilization, and the finite element method is one of the most useful methods for numerical simulation. To apply finite element solution, we need decompose the problem domain (the region on which the problem is defined) into figures called finite elements. The decomposition of the problem domain is called triangulation. It has been well known that, to obtain accurate numerical solutions, we need to impose some geometric conditions on triangulations.
It has been cleared by our research that the most important factor is the maximum of the radius of triangles in the triangulation. We have shown that if the maximum of the circumradius converges to 0, then the error of finite element solution converges to 0.
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| Academic Significance and Societal Importance of the Research Achievements |
有限要素法により数値シミュレーションを行う場合、もっとも大変なのは問題領域の三角形分割であると言われている。本研究により三角形分割の幾何学的形状のついての最も重要な条件が、分割内の三角形の外接半径の最大値であることがわかった。この条件は、今まで知られていた「正則性条件」や「最大角条件」よりも緩く、三角形分割にかかる計算量を軽減できることが期待できる。また、得られた条件はすぐに３次元の場合に拡張できることが期待できる。
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