2010 Fiscal Year Final Research Report

On structure-preserving numerical methods on complex domains

Research Project

Project/Area Number	20760052
Research Category	Grant-in-Aid for Young Scientists (B)
Allocation Type	Single-year Grants
Research Field	Engineering fundamentals
Research Institution	The University of Tokyo
Principal Investigator	MATSUO Takayasu The University of Tokyo, 大学院・情報理工学系研究科, 准教授 (90293670)
Project Period (FY)	2008 – 2010
Keywords	数理工学 / 数値解析 / シミュレーション
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.

(6 results)