Xianzheng Jia
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Xianzheng Jia has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Xusheng Li
School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China
1 shared publication - Zhenyu Zhao
School of Mathematics and Statistics, Shandong University of Technology, Zibo, China
1 shared publication
Latest Publications
- Open Access
Reconstruction of Piecewise Smooth Functions Based on Fourier Extension
This paper proposes a hierarchical Fourier extension framework for the accurate reconstruction of piecewise smooth functions with mixed-order singularities. To address key challenges in spectral approximation–namely boundary-induced artifacts, instability in edge detection, and loss of accuracy near discontinuities–the method integrates three main components: (1) boundary-focused Fourier extensions that isolate endpoint effects while preserving internal structures; (2) a multi-stage edge detection strategy combining spectral mollifiers and coordinate transformations to identify discontinuities in function values and their derivatives; (3) adaptive domain partitioning followed by localized Fourier extensions to retain spectral accuracy on smooth segments. Numerical results demonstrate near machine-precision accuracy (∼10−14–10−15) with significantly improved stability and performance over traditional global methods.
Open AccessReconstruction of Piecewise Smooth Functions Based on Fourier Extension
This paper proposes a hierarchical Fourier extension framework for the accurate reconstruction of piecewise smooth functions with mixed-order singularities. To address key challenges in spectral approximation–namely boundary-induced artifacts, instability in edge detection, and loss of accuracy near discontinuities–the method integrates three main components: (1) boundary-focused Fourier extensions that isolate endpoint effects while preserving internal structures; (2) a multi-stage edge detection strategy combining spectral mollifiers and coordinate transformations to identify discontinuities in function values and their derivatives; (3) adaptive domain partitioning followed by localized Fourier extensions to retain spectral accuracy on smooth segments. Numerical results demonstrate near machine-precision accuracy (∼10−14–10−15) with significantly improved stability and performance over traditional global methods.