2013 Fiscal Year Final Research Report
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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| Keywords | 数理工学 / 数値解析 |
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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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