arXiv subjects

Hirofumi Tomita

Publications and source records attributed to Hirofumi Tomita.

3 recordsLinked to original sources

arXiv2026

Design Principle for Mode-Consistent Galerkin Closure under a Physical Energy Metric for Hyperbolic Systems

This paper derives a design principle for structure-preserving Galerkin formulations of energy-conserving hyperbolic systems. The aim is to reproduce the modal-energy-exchange structure of the continuous system within a resolved finite-mode space. Total energy conservation follows from this structure. We introduce a state-dependent physical-energy metric H and derive the corresponding energy-compatibility identity. In the infinite-mode exact-integration model, the volume contribution has an antisymmetric representation after H-orthogonalization, yielding pairwise modal energy exchange. Interface contributions take the same exchange form. To reproduce this structure in the practical finite-mode system, we combine two constructions: a Galerkin projection coupled with the physical-energy metric that guarantees the H-metric summation-by-parts identity, and an energy-compatibility closure that removes the component of the compatibility action contributing to the scalar energy residual. With a shared numerical energy flux at interfaces, they close the total-energy balance of the finite-mode system while preserving pairwise modal energy exchange. We also compare the practical operator construction with the finite-mode exact-integration reference and obtain an O(h^p+1) defect estimate. Finally, we derive an equivalent form of the resulting equation in the fixed Galerkin basis for direct implementation.

math.NA↗

arXiv2026

Learning-Augmented Performance Model for Tensor Product Factorization in High-Order FEM

Accurate performance prediction is essential for optimizing scientific applications on modern high-performance computing (HPC) architectures. Widely used performance models primarily focus on cache and memory bandwidth, which is suitable for many memory-bound workloads. However, it is unsuitable for highly arithmetic intensive cases such as the sum-factorization with tensor $n$-mode product kernels, which are an optimization technique for high-order finite element methods (FEM). On processors with relatively high single instruction multiple data (SIMD) instruction latency, such as the Fujitsu A64FX, the performance of these kernels is strongly influenced by loop-body splitting strategies. Memory-bandwidth-oriented models are therefore not appropriate for evaluating these splitting configurations, and a model that directly reflects instruction-level efficiency is required. To address this need, we develop a dependency-chain-based analytical formulation that links loop-splitting configurations to instruction dependencies in the tensor $n$-mode product kernel. We further use XGBoost to estimate key parameters in the analytical model that are difficult to model explicitly. Evaluations show that the learning-augmented model outperforms the widely used standard Roofline and Execution-Cache-Memory (ECM) models. On the Fujitsu A64FX processor, the learning-augmented model achieves mean absolute percentage errors (MAPE) between 1% and 24% for polynomial orders ($P$) from 1 to 15. In comparison, the standard Roofline and ECM models yield errors of 42%-256% and 5%-117%, respectively. On the Intel Xeon Gold 6230 processor, the learning-augmented model achieves MAPE values from 1% to 13% for $P$=1 to $P$=14, and 24% at $P$=15. In contrast, the standard Roofline and ECM models produce errors of 1%-73% and 8%-112% for $P$=1 to $P$=15, respectively.

cs.DC↗

arXiv2025

Nonlocally coupled moisture model for convective self-aggregation

Clouds play a central role in climate physics by interacting with precipitation, radiation, and circulation. Despite being a fundamental issue in convective organization, the self-aggregation of clouds lacks a theoretical explanation due to its complexity. In this study, we introduce an idealized mathematical model where the system's state is represented solely by the vertically integrated water vapor content of atmospheric columns under the weak temperature gradient approximation. By analyzing the nonlinear dynamics of this simplified system, we mathematically elucidate the mechanisms that determine the onset of self-aggregation and the spatial scale of the self-aggregated state. Nonlocal coupling between atmospheric columns induces bistability, leading to dry and moist equilibria. This reflects the circulation effects driven by horizontal differential heating due to convection and radiation. The bistable self-aggregated state realizes when destabilization by nonlocal coupling, triggered by finite-amplitude disturbances in the uniform state, overcomes stabilization by diffusion. For globally coupled systems where all columns are equally coupled, perturbations with the maximum wavelength exhibit the highest growth rate. This results in a solution with an infinitely long wavelength, understood as the dynamical system's heteroclinic trajectories describing the steady state's spatial evolution. Conversely, for nonlocally coupled systems with finite filter lengths, perturbations with wavelengths close to the characteristic length of the coupling are preferred. The results reveal that the balance between nonlocal coupling and diffusion is essential for understanding convective self-aggregation. Moreover, this study suggests a physical similarity between convective self-aggregation and moisture mode.

physics.ao-ph↗