2021 Fiscal Year Research-status Report
Multisymplectic Geometry and Geometric Numerical Integrator for Variational Problems
| Project/Area Number |
20K14365
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| Research Institution | Keio University |
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Principal Investigator |
彭 林玉 慶應義塾大学, 理工学部(矢上), 講師 (90725780)
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | Noether's theorem / Symmetry / Conservation law / DPD / Hamiltonian system |
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| Outline of Annual Research Achievements |
Firstly, we extended Noether’s theorems to semi-discrete equations: the first theorem connecting variational symmetries and conservation laws while the second one dealing with infinite-dimensional symmetries. At the same time, theoretic developments of the current project were applied to dissipative particle dynamics by constructing novel structure-preserving numerical methods for stochastic Hamiltonian systems with external forces. These results are published or accepted for publication in peer-reviewed journals.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
The project is running smoothly with the publication of 4 peer-reviewed papers in leading academic journals and a couple of invited conference/workshop presentations.
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| Strategy for Future Research Activity |
The research will be continued following the original proposal. In particular, we will apply the modified formal Lagrangian formulation proposed in the current project for developing geometric integrator of non-variational equations.
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| Causes of Carryover |
International travel seems finally possible. The principal investigator and/or research students of his group are planning to visit abroad to continue international collaborations.
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