arXiv subjects

Youngsoo Ha

Publications and source records attributed to Youngsoo Ha.

4 recordsLinked to original sources

arXiv2026

Drift-Free Conservative Dynamics from Quantized Interaction Rules

Conservation laws are conventionally discretized through floating-point flux evaluation, with invariants obtained by cancellation of approximate interface contributions and admissible weak solutions selected by reconstruction and Riemann solvers. Here we introduce an operator-level formulation in which conservative dynamics is realized as an exact discrete interaction rule on a quantized state space. The update is defined by an antisymmetric integer-transfer operator, which enforces conservation exactly at the arithmetic level and eliminates round-off drift from the primitive evolution. For scalar laws, monotone order-preserving transfers select admissible shock structures within the primitive update, rather than through flux reconstruction. Numerical experiments show that the interaction rule preserves high-frequency transport near the Nyquist limit and maintains sharply localized discontinuities in Burgers dynamics. The same construction extends to multidimensional problems and systems of conservation laws through oriented, vector-valued integer transfers. The results show that exact integer-transfer dynamics can suppress cumulative transport drift while preserving entropy-shock localization in nonlinear conservative evolution.

math.NA↗

arXiv2026

Continuum dynamics from quantised interaction rules

Hyperbolic conservation laws are conventionally solved by evolving reconstructed floating-point fields, incurring both computational overhead and structural diffusion near discontinuities. Here we introduce the Fast Quantised Numerical Method (FQNM), in which the conservative operator is realised directly as an antisymmetric integer transfer rule on a countable state space, with continuum fields appearing only as reconstructed observables. For scalar conservation laws with monotone flux splitting, we establish exact conservation, monotonicity, TVD and $L^1$ stability, and convergence of the reconstructed solution to the entropy solution under $\delta/\Delta x \to 0$. We further show that distinct classical flux formulations collapse to identical dynamics whenever they induce the same integer transfer rule, identifying the transfer operator as the effective computational object. Across representative regimes, FQNM remains stable near the Nyquist limit in high-frequency transport, preserves grid-level shock structure in Burgers dynamics, and in a matched Roe-flux Sod prototype preserves shock structure at the density-scale conserved-state level relative to an exact Riemann reference, while achieving order-of-magnitude prototype acceleration over floating-point baselines. These results demonstrate that, for conservative hyperbolic dynamics, executing the operator as quantised transfer rather than reconstructed field evolution can simultaneously alter structural fidelity and reduce computational cost, establishing a new representation paradigm for conservation-law solvers.

math.NA↗

arXiv2024

Neural Operators Learn the Local Physics of Magnetohydrodynamics

Magnetohydrodynamics (MHD) plays a pivotal role in describing the dynamics of plasma and conductive fluids, essential for understanding phenomena such as the structure and evolution of stars and galaxies, and in nuclear fusion for plasma motion through ideal MHD equations. Solving these hyperbolic PDEs requires sophisticated numerical methods, presenting computational challenges due to complex structures and high costs. Recent advances introduce neural operators like the Fourier Neural Operator (FNO) as surrogate models for traditional numerical analyses. This study explores a modified Flux Fourier neural operator model to approximate the numerical flux of ideal MHD, offering a novel approach that outperforms existing neural operator models by enabling continuous inference, generalization outside sampled distributions, and faster computation compared to classical numerical schemes.

physics.comp-ph↗

arXiv2020

Improving accuracy of the fifth-order WENO scheme by using the exponential approximation space

The aim of this study is to develop a novel WENO scheme that improves the performance of the well-known fifth-order WENO methods. The approximation space consists of exponential polynomials with a tension parameter that may be optimized to fit the the specific feature of the data, yielding better results compared to the polynomial approximation space. However, finding an optimal tension parameter is a very important and difficult problem, indeed a topic of active research. In this regard, this study introduces a practical approach to determine an optimal tension parameter by taking into account the relationship between the tension parameter and the accuracy of the exponential polynomial interpolation under the setting of the fifth-order WENO scheme. As a result, the proposed WENO scheme attains an improved order of accuracy (that is, sixth-order) better than other fifth-order WENO methods without loss of accuracy at critical points. A detailed analysis is provided to verify the improved convergence rate. Further, we present modified nonlinear weights based on $L^1$-norm approach along with a new global smoothness indicator. The proposed nonlinear weights reduce numerical dissipation significantly, while attaining better resolution in smooth regions. Some experimental results for various benchmark test problems are presented to demonstrate the ability of the new scheme.

math.NA↗