S-version of finite element method (SFEM) has intrinsic advantages of local high accuracy, low computation time, and simple meshing procedure, because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial resolutions. However, the conventional SFEM has disadvantages such as accuracy of numerical integration and matrix singularity. Thus, we have proposed a new framework, B-spline SFEM (BSFEM), which solves their problems, and improves the accuracy and the convergence of matrix calculations. On the other hand, to analyze larger problems, parallel programming with message passing interface (MPI) is necessary, assuming the use of distributed memory parallel computers. However, there are few studies on parallelization of SFEM, especially applying domain decomposition methods commonly used in finite element methods due to the complexity of its mesh structure. In this study, parallel computing of BSFEM is realized by generalizing the complex mesh structure into a graph that represents the interaction between computation nodes. To evaluate its parallel performance, we performed strong scaling tests.

This study improves and generalizes the ghost cell boundary (GCB) model, which calculates the wall boundary contribution by using cells (elements) and the Gaussian quadrature, focusing on free surface flow analysis using particle methods. The proposed method is applicable to semi-implicit type particle methods including the stabilized ISPH and can use an arbitrary number of integration points. We also clarify how to apply formulation of the fixed ghost particle to the integral points of the GCB model and realize the strict imposition of the wall boundary condition, which has been a problem in conventional methods. The accuracy and versatility of the proposed method are verified by the hydrostatic pressure and dam break problems.

Reduced Order Modeling (ROM) reduces the computational cost in simulating physics phenomena by using reduced dimensional spaces. However, it becomes difficult to apply ROM to reconstruction of physical fields represented by the Lagrangian mechanics, such as the particle method, in the numerical analysis of free surface flows. This study aims to create a ROM applicable to free surface flows of Lagrangian description. A novel deep learning-based mode decomposition method, which can be applied to simulate physics phenomena obtained by the Lagrange method, is proposed as a component of ROM in this paper. Validation of proposed method was carried out for the analysis of water drop problem. The results showed that the original physical field can be reconstructed with high accuracies from the modes obtained by NMD realized deep learning.

本研究では，梁要素を用いたFEMにおける幾何学的に精緻な接触計算手法を提案する．提案手法では，梁要素が表す部材の表面形状を粒子で離散的に表現し，粒子間に力学的・幾何学的な接触拘束条件を課す．そのうえで，要素の節点と粒子間の幾何学的関係に基づき，粒子間の接触拘束をFEMのつり合い式に組み込む要素間の接触拘束に帰着させる．このアプローチにより，部材に大変形やねじりのような複雑な変形が生じている場合でも，部材表面の面的な接触を容易に解くことができる．提案手法を用いて梁部材の静的・動的接触問題の数値計算例を解くことにより，その妥当性および有用性を示す．

物理現象は複数の場が相互作用する連成現象であり、その理解と予測には数値シミュレーションが広く利用される。

近年計算機の性能向上により、大規模なシミュレーションと可視化が可能になった。大規模な解析対象の可視化は、注目領域の特定が難しく、インタラクティブ可視化が重要な役割をもつ。

特に連成解析では、対象に応じて異なる数値計算手法が用いられ、計算結果の汎用的な可視化は容易ではない。

本研究では、これらの問題を解決するために、数値解析手法に依存しない汎用的な大規模データ可視化システムを提案する。

陰関数表現を用いたマーチングキューブ法に分散メモリ並列処理を適用し、その性能を評価した。

並列性能評価から、提案システムが高い並列性能を持つことが確認された。