A study of a high accurate numerical method for the inverse problem in the wave equation
| Project/Area Number |
23540152
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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 | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Aichi Prefectural University |
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Principal Investigator |
SHIROTA Kenji 愛知県立大学, 情報科学部, 准教授 (90302322)
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 非適切問題 / 高精度解法 / 波動場 / 数値的再構成手法 / 多倍長計算 / 密度型位相最適化問題 / 任意多点差分法 / H1勾配法 / 数値的再構成法 / 最適設計問題 / 抽象勾配法 / 欠陥同定問題 / 波動方程式 / 逆問題 / 密度型トポロジー最適化問題 / モデル化誤差 / 超高精度解法 |
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| Outline of Final Research Achievements |
In this research, we considered about the numerical method to get a high accurate approximated solutions to the initial-boundary value problem in scalar wave equation. We apply the lattice-free finite difference method and the spectral collocation method with the Gauss-Lobatto points to the discretization in space and time direction, respectively. We show the effectiveness of our method by some numerical experiments.
Moreover, we consider a high accurate method for SIMP type topology optimization problem. We adopt the H1 gradient method to solve our problem. In order to get high accurate solution of the partial differential equation in our algorithm, we use the lattice-free finite difference method. By the numerical experiments, we check the effectiveness, stability, and convergency of our algorithm.
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Report
(6 results)
Research Products
(11 results)
