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Weifeng Hou

Publications and source records attributed to Weifeng Hou.

2 recordsLinked to original sources
arXiv2026

Mathematical foundation of symmetric fast Fourier transform

In this work, we study the fast Fourier transform (FFT) of discrete data with crystallographic symmetry, for which standard FFT algorithms incur substantial redundant computation. We establish a rigorous mathematical theory of the symmetric fast Fourier transform (SFFT) for $n$-dimensional crystallographic groups and propose the SFFT and symmetric inverse fast Fourier transform (SIFFT) algorithms. We derive symmetry-reduction formulas for both linear and translational symmetries and unify them into a recursive framework. We analyze the arithmetic complexity to obtain theoretical speedup factors relative to the standard FFT, and we confirm the accuracy and efficiency of the proposed methods by numerical experiments on representative three-dimensional space groups.

math.NA↗
arXiv2026

A Globally Conservative Compact Framework for Conservation Laws: Fourth-Order Schemes with Enhanced Resolution and Stability

The compact finite difference method is a powerful tool for discretizing conservation laws, owing to its inherent flexibility in developing high-resolution and highly stable schemes. In this paper, we propose a framework for the design of genuine globally conservative compact finite difference schemes, which addresses a critical requirement in conservation laws. Within our framework, we rigorously establish that the discrete conservation law maintains strict conservation for flux functions in polynomial spaces with optimal algebraic order, i.e., the discrete scheme achieves an optimal algebraic precision.Our work advances the existing conservative compact finite difference schemes, which rely on approaches to maintaining global conservation that are fundamentally consistent with the method proposed by Lele [Lele, J. Comput. Phys., 1992]. As an application, we propose an algorithm for designing globally conservative fourth-order schemes, aimed at optimizing resolution and asymptotic stability. Three schemes are generated using the algorithm, with their excellent performance across multiple aspects validated through numerical experiments.

math.NA↗