arXiv subjects

Naoki Morita

Publications and source records attributed to Naoki Morita.

5 recordsLinked to original sources

arXiv2026

A hybrid s-version isogeometric strategy for dynamic crack propagation in 2D and 3D problems

A hybrid s-version of isogeometric analysis (hS-IGA) strategy is proposed for accurate and efficient evaluation of near-crack fracture quantities in dynamic crack propagation analysis. The strategy retains the global-local superposition framework of the conventional s-method, while introducing B-spline basis functions only into the global discretisation and preserving a Lagrange-based local mesh in the crack domain. This hybrid formulation is motivated by the continuity-related bottleneck in the global-local coupling integration of the conventional Lagrange-based s-method, and by the need to retain a Lagrange-based local mesh for crack representation and post-processing of the dynamic stress intensity factor (DSIF) and local stress. The resulting formulation removes discontinuities in the coupling integrands caused by the global approximation and enables accurate coupling integration by standard Gauss quadrature without recursive subdivision. The proposed strategy is verified using two-dimensional stationary and dynamic straight-crack problems against the standard finite element method and the conventional s-method, and is further assessed using three-dimensional stationary and dynamically propagating circular-crack problems against the conventional s-method. Results show that the proposed hS-IGA strategy accurately evaluates the DSIF and local stress while retaining the global-local modelling advantages of the s-method. It also substantially reduces the number of integration points required for coupling integration, by approximately 81% in the two-dimensional dynamic benchmark and 95.6% in the three-dimensional dynamic benchmark relative to the conventional s-method. These results demonstrate that the proposed hS-IGA framework provides an accurate and efficient global-local strategy for dynamic crack propagation analyses requiring reliable evaluation of near-crack fracture quantities.

cs.CE↗

arXiv2026

Metagraph-Based Domain-Decomposed Galerkin Reduced-Order Model

This study proposes a metagraph-based domain-decomposed Galerkin reduced-order model (MBDD-G-ROM) for distributed-memory parallel reduced-order analysis of large-scale problems. The method represents domain-decomposed Galerkin reduced-order models over arbitrary domain decompositions using two graph levels: calculation-point graphs for interactions among discretization points and metagraphs for connectivity among local approximation-space subdomains. In the proper orthogonal decomposition (POD)-based implementation, POD computation subdomains are represented as metanodes, while metaedges encode the block-sparsity induced by overlaps between local POD basis supports. Partitioning the metagraph enables the POD computation subdomains to be decoupled from the parallel computation subdomains, allowing distributed-memory parallelization of both offline and online phases, including reduced-system assembly and iterative linear solution, without requiring the two decompositions to coincide. The metagraph also supports static load balancing through metanode weights that approximate computational costs. The method is evaluated for an unsteady diffusion equation and incompressible Navier-Stokes flow around a three-dimensional cylinder. The results show that MBDD-G-ROM preserves reduced-order solution accuracy while achieving high online parallel efficiency. A load-balancing test further demonstrates that cost-based metanode weights can improve computational efficiency.

math.NA↗

arXiv2026

Domain-decomposed parallelization of B-spline based s-version of the finite element method via generalized graph abstraction

The s-version of the finite element method (SFEM) enables locally high-resolution analysis by superimposing independently defined finite element meshes. However, domain-decomposed parallelization is nontrivial because complex interactions arise among degrees of freedom distributed over multiple meshes. In this study, we propose a method for constructing a graph structure that uniformly represents interactions among computational points, including both intra- and inter-mesh interactions, based on the overlap of basis-function supports. We apply the proposed graph representation to the B-spline based SFEM (BSFEM), a high-accuracy SFEM formulation previously proposed by the authors. The resulting graph partition enables the consistent assignment of degrees of freedom and elements to processes and the construction of the MPI communication structure, thereby realizing domain-decomposition-based distributed-memory parallelization of BSFEM. To the best of the authors' knowledge, this BSFEM implementation constitutes the first domain-decomposition-based distributed-memory parallelization of an SFEM-based method. Furthermore, as an example demonstrating the utility of the proposed graph representation, we apply cost-weighted graph partitioning in which the matrix-generation costs specific to BSFEM are incorporated into node weights, and demonstrate effective static load balancing that accounts for the nonuniform matrix-generation workload.

math.NA↗

arXiv2023

Higher-continuity s-version of finite element method with B-spline functions

This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial resolutions, it has intrinsic advantages of local high accuracy, low computation time, and simple meshing procedure. However, it has disadvantages such as accuracy of numerical integration and matrix singularity. Although several additional techniques have been proposed to mitigate these limitations, they are computationally expensive or ad-hoc, and detract from its strengths. To solve these issues, we propose a novel strategy called B-spline based SFEM. To improve the accuracy of numerical integration, we employed cubic B-spline basis functions with $C^2$-continuity across element boundaries as the global basis functions. To avoid matrix singularity, we applied different basis functions to different meshes. Specifically, we employed the Lagrange basis functions as local basis functions. The numerical results indicate that using the proposed method, numerical integration can be calculated with sufficient accuracy without any additional techniques used in conventional SFEM. Furthermore, the proposed method avoids matrix singularity and is superior to conventional methods in terms of convergence for solving linear equations. Therefore, the proposed method has the potential to reduce computation time while maintaining a comparable accuracy to conventional SFEM.

math.NA↗

arXiv2021

Isometric Transformation Invariant and Equivariant Graph Convolutional Networks

Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial requirement for applying graphs in Euclidean spaces to physical simulations is learning and inferring the isometric transformation invariant and equivariant features in a computationally efficient manner. In this paper, we propose a set of transformation invariant and equivariant models based on graph convolutional networks, called IsoGCNs. We demonstrate that the proposed model has a competitive performance compared to state-of-the-art methods on tasks related to geometrical and physical simulation data. Moreover, the proposed model can scale up to graphs with 1M vertices and conduct an inference faster than a conventional finite element analysis, which the existing equivariant models cannot achieve.

cs.LG↗