Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao/Journal of Computer-Aided Design and Computer Graphics 27(4) 590-596 2015年4月 [査読有り]
Traditional structural optimization methods require predefined load conditions. The resulting structure is optimal under the given condition, but can be weak under different loads. Objects can suffer from various forces in practical applications. ...
Kazuaki Tanaka Akitoshi Takayasu Xuefeng Liu Shin'ichi Oishi
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 31(3) 665-679 2014年11月 [査読有り]
This paper proposes a verified numerical method of proving the invertibility of linear elliptic operators. This method also provides a verified norm estimation for the inverse operators. This type of estimation is important for verified computatio...
For Poisson's equation over a polygonal domain of general shape, the solution of which may have a singularity around re-entrant corners, we provide an explicit a priori error estimate for the approximate solution obtained by finite element methods...
SIAM JOURNAL ON NUMERICAL ANALYSIS 51(3) 1634-1654 2013年 [査読有り]
The finite element method (FEM) is applied to bound leading eigenvalues of the Laplace operator over polygonal domains. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domains of symme...
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 30(3) 635-652 2013年 [査読有り]
We consider an explicit estimation for error constants from two basic constant interpolations on triangular finite elements. The problem of estimating the interpolation constants is related to the eigenvalue problems of the Laplacian with certain ...
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