2010 Fiscal Year Final Research Report
On structure-preserving numerical methods on complex domains
| Project/Area Number |
20760052
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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 | The University of Tokyo |
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Principal Investigator |
MATSUO Takayasu The University of Tokyo, 大学院・情報理工学系研究科, 准教授 (90293670)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 数理工学 / 数値解析 / シミュレーション |
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| Research Abstract |
In this research, we aimed at extending the discrete variational derivative method to finite element framework, and got the following results.
First, we showed that in the spatially one-dimensional case a finite-element version of the discrete variational derivative method can be formulated only with H^1 elements, and in fact applied the new framework to several typical partial differential equations. Then we extended the framework to spatially two-/three-dimensional cases, where we applied the method to the Ginzburg-Landau equation and confirmed the scheme in fact successfully works. Finally, we introduced a new technique to linearize the resulting schemes, and checked by numerical experiments that computational complexity can be decreased.
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