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.

The discontinuous Galerkin (DG) method is effective and promising tool for the hyperbolic equations with discontinuities. In recent years, the DG method has been applied and shown to be effective in the analysis of shallow water equations (SWEs), which are widely used for river flooding, storm surge, tsunami, and other natural disaster simulations. In this study, the DG method is applied to the governing equations for riverbed variation, which are coupling of the SWEs and equilibrium sediment transport equation, and wetting-drying treatment and numerical flux are discussed for our purpose. The proposed method has been verified with numerical analysis such as erodible dam-break flow and sandbar migration simulation. The numerical results have shown that the proposed method is effective for riverbed variation analysis.

While the particle method is suitable for representation of large and discontinuous deformations, it is prone to accuracy degradation and numerical instability due to issues with particle distribution. To solve this problem, SPH(2) has been proposed, which can perform highly accurate calculations even when there are disturbances in the particle distribution. But is still limited in overcoming numerical instability. From previous studies, it is found that more stable and accurate calculations can be achieved by using SPH(2) in combination with the particle shifting technique. However, the existing particle shifting technique tends to expand the volume in the long term smulations. Therefore, we propose a new particle rearrangement method that can simultaneously improve particle homogeneous distribution and volume conservation. For this purpose, it is also important to use the proposed method in combination with other stabilization techniques, and our policy is to sort out the roles of various stabilization techniques and eliminate unnecessary terms. In addition, the numerical stability and accuracy improvement of the proposed method are demonstrated by Rotating square patch fluid simulations and Dam break simulations.

This paper provides a survey on prominent libraries that enable parallel simulations, with a focus on their applicability for research and development purposes. It discusses the functionalities and scope of these libraries with respect to range of numerical methods to which they can be applied. Following an overview and discussion of libraries, this paper introduces a unified library designed for domain-decomposition based parallel simulations. The unified library is based on graph structures representing the interactions between computational points in numerical simulations, aiming to be applicable to a wide variety of numerical methods. As applications of the graph-based unified library, the paper presents standard finite element method (mesh-based method), particle method (mesh-free method), and s-version finite element method that allows for the overlay of multiple meshes within the finite element framework. The parallel computing performance of these methods is also discussed.

In this study, the effects of nesting and laminate misalignment on the resin permeability of woven composites are investigated using an asymptotic homogenization method for permeation flow. For this, a meso-scale unit cell model consisting of two hexagonal prisms with four fiber bundles and periodic boundary conditions for the unit cell are proposed to explicitly consider the nesting and laminate misalignment. This method enables to deal with arbitrary amounts of nesting and laminate misalignment easily, which has been difficult in the case of using conventional cuboid unit cells. The unit cell and boundary conditions are then applied to the homogenization method for permeation flow, and resin permeability analysis of plain-woven glass fiber-reinforced plastic (GFRP) composites are conducted. It is shown from the results that the nesting affects the mesoscopic characteristic flow velocity and the macroscopic resin permeability, and that they tend to decrease with increase in nesting. It is also shown that the laminate misalignment significantly affects the distribution of mesoscopic characteristic flow velocity and the macroscopic resin permeability, and that a combination of nesting and laminate misalignment can successfully reproduce experimentally observed macroscopic resin permeabilities of plain-woven GFRP composites.

We propose a deep generative model for 3D shapes that incorporates structural mechanics parameters, and a dataset of 6667 shapes created by topology optimization. Our model is based on DeepSDF, a decoder-type neural network that implicitly represents shapes as signed distance functions (SDFs). We extend DeepSDF to condition the shape generation on structural mechanics parameters, such as strain energy, load direction, volume, and dimension. We also introduce positional encoding to improve the spatial resolution of the model. Our dataset consists of various 3D shapes computed by a linear topology optimization method using the Building-Cube method. We use the strain energy as a quantitative indicator of the structural performance of the shapes. We train our model on the dataset and evaluate its ability to generate 3D shapes reflecting structural mechanics parameters. Our results indicate that our model can produce 3D shapes with high fidelity and diversity, and achieve an average reconstruction accuracy of 88.8% for the test shapes. Our model and dataset open up new possibilities for 3D shape generation and structural design using deep learning.

The Deflated Conjugate Gradient (DCG) method represents is one of preconditioned conjugate gradient method that utilize of known linearly independent vectors. The study proposes subdomain eigenmode deflation preconditioning that employs low-order eigenmodes, obtained from eigenvalue analysis within partitioned domains of parallel finite element analysis, as a set of deflation vectors for the DCG method. The parallel performance of the proposed method is evaluated by the number of iterations required for convergence and the total computation time through its application in structural analysis. Compared to the standard conjugate gradient method, the proposed method reduces the total computation time by up to 85 %.