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.

In this research, geometrically exact contact calculation method for FEM using beam element is proposed. The proposed method discretely represents surface shape of beam by particles and imposes mechanical and geometric constraints of contact between particles. Since the particles and element nodes are geometrically related, the contact constraint conditions between the particles can be yielded into the equation of motion as the constraints defined between the elements. This approach allows to easily resolve geometrically complex contact configurations even if large and complex deformation such as torsion is occurred. Validity and usefulness of the proposed method is indicated by solving numerical examples of static or dynamic contact problems of beams.

Physical phenomena are complex interactions among multiple fields, and numerical simulations are widely used to comprehend and predict them. With the improvements of computational capabilities, it has become feasible to perform large-scale simulations and visualizations. However, large-scale visualization poses challenges in identifying the region of interest, necessitating the interactive visualization. Particularly in coupled analyses, various discretization methods is employed depending on their application. This study proposes a general-purpose large-scale visualization system that is not depend on specific numerical analysis methodologies. It transforms computational results into implicit function representations and applies distributed-memory parallel processing to the marching cubes method. The evaluation of parallel computing performance confirms that the proposed system has reasonable parallel efficiency.