New energy-preserving numerical schemes for Hamiltonian PDEs and formulation of the framework as a discrete mechanics
| Project/Area Number |
22760060
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Engineering fundamentals
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| Research Institution | Kobe University (2011-2013)
The University of Tokyo (2010) |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 数理工学 / 数値解析 / 構造保存型数値解法 / 解析力学 / 幾何学的力学理論 / 有限要素法 / 離散微分形式 / 有限差分法 / 対称性 / 保存則 / 離散勾配法 / Noetherの定理 / エネルギー保存則 / 運動量保存則 / ハミルトン偏微分方程式 |
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| Research Abstract |
In this research, we proposed a new framework for deriving energy-preserving numerical schemes for Hamiltonian partial differential equations. In our framework, energy-preserving schemes are derived by using the symmetry of time translation of the Lagrangian that defines the equation. Since the symmetry used in this framework is not restricted to that of time translation, this method also derives numerical schemes that inherit other conservation laws by using the corresponding symmetries. Extension of this method to systems with holonomic constraints, local discrete conservation laws of the schemes and combination with the finite element exterior calculus were also investigated.
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Report
(5 results)
Research Products
(61 results)
