亀裂の生成や進展現象を解析可能な数値解析手法にペリダイナミック（PD）がある．しかし，破壊を特徴づける重要なパラメータであるエネルギ解放率に関するPDの研究は数多くない．さらに，PDは非局所理論に基づいた積分方程式を解く解析手法であることから境界付近では計算精度が悪くなることが知られている．その問題を避けるため，4つのPDの定式化を用いてE積分公式を適用しエネルギ解放率を求めて理論解との比較を行った．その結果，NOSB-PDとFEMの連成解析に対して高精度でエネルギ解放率が得られ，積分経路をFEM領域に限ることで高精度で経路独立性が得られることを示した．

This study proposes novel conservative filters for uniformly spaced grids. The original conservative filters, proposed by Vreman, are extended by developing a filter matrix that is symmetric stochastic and pentadiagonal, rather than tridiagonal. When the original conservative filters are applied to uniform grids, once the coefficients of the filters at the interior nodes are established, the coefficients of the filter at the boundary can be determined uniquely. This study improves the flexibility of adjusting the filter strength near the boundaries. The numerical results suggest that the developed filters can be applied when it is essential that filters neither increase the global maximum nor decrease the global minimum of a variable.

We propose an ellipsoidal particle model for the Moving Particle Hydrodynamics (MPH) method to reduce the computational cost in thin calculation geometries. The Lagrangian and dissipation functions of the MPH method are extended for an ellipsoidal particle model, which has an ellipsoidal influence domain. The governing equations of the ellipsoidal MPH method are derived from the extended Lagrangian with dissipation. The proposed ellipsoidal MPH method was applied to calculate a hydrostatic problem, the evolution of a droplet, and a dam break problem. The results of the former two calculations showed good agreement with the theoretical solutions. In the dam break calculation, the front position agreed well with the experiment, both with and without the ellipsoidal particle model. However, the dependence on the aspect ratio of the ellipsoidal particle was observed in the shape of splashes.