著者

堀江 正信 森田 直樹 井原 遊 三目 直登

出版者

一般社団法人 日本計算工学会

雑誌

日本計算工学会論文集 (ISSN:13478826)

巻号頁・発行日

vol.2020, no.1, pp.20201005, 2020-11-13 (Released:2020-11-13)

参考文献数

26

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メッシュは有限要素法や有限体積法で用いられる重要なデータ構造である.メッシュデータ構造はグラフと呼ばれるデータ構造の一種であるとみなせるため,メッシュを学習するために graph neural network (GNN) が広く用いられてきた.本研究では,GNN が有限要素解析の学習に有用なモデルであることを示す.提案手法では,メッシュの回転や並進に対して不変となるような形状の特徴量を入力として用いることによって学習をより効率的にしている.さらに,提案手法は学習データセットに含まれていない 100 万節点もの大きなメッシュに対しても精度を有意に落とすことなく推論ができることがわかった.

著者

堀江 正信

出版者

株式会社RICOS

雑誌

学術変革領域研究(A)

巻号頁・発行日

2023-04-01

著者

森田 直樹 堀江 正信 須藤 海

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 (ISSN:21879761)

巻号頁・発行日

vol.86, no.882, pp.19-00337, 2020 (Released:2020-02-25)

参考文献数

22

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In numerical analyses based on unstructured meshes represented by the finite element method, quadrilateral and hexa-hedral meshes are used for a two-dimensional and a three-dimensional analyses, respectively, from the viewpoint of calculation accuracy and computation time. However, a method for automatically generating quadrilateral and hexahedral meshes has not been established thus far; in addition, a considerable amount of effort is required to perform manual mesh modifications. Mesh generation based on the frame field method is an effective technique to extract high quality quadrilateral and hexahedral meshes through the optimization of the posture of a frame with rotational symmetry. This method needs to solve a mixed-integer programming (MIP) problem while extracting the quadrilateral and hexahedral mesh using integer grid maps. When solving an MIP using a greedy method, solving a simultaneous equation is required approximately O(M) times, where M is the number of integer constraints. In this study, we propose a method to obtain a quadrilateral mesh by solving a simultaneous equation approximately O(1) times. In this method, the frame field is calculated using finite element discretization, and the finite element mesh is appropriately remeshed to be aligned with the integer grid resulting from the frame field optimization. The proposed method can reduce the amount of computation required to obtain integer grid maps for mesh extraction, without impairing the mesh quality. The proposed method is evaluated with respect to by mesh quality using the aspect ratio and the scaled Jacobian. Numerical examples demonstrate that the mesh quality is comparable to or better than that produced by conventional methods and manual procedures.