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Mathematics
Special Issues
Numerical and Computational Methods in Engineering, 2nd Edition
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Numerical and Computational Methods in Engineering, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 31 October 2026 | Viewed by 562

Special Issue Editors

Prof. Dr. Qinghe Yao

E-Mail Website
Guest Editor
School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, China
Interests: efficient numerical-driven parallel solution algorithm; multi-field coupling; high-fidelity numerical models; large-scale computational mechanics algorithm; engineering application
Special Issues, Collections and Topics in MDPI journals
Dr. Weide Liu

E-Mail Website
Guest Editor
School of Mathematical Sciences, Guangxi Minzu University, Nanning 530006, China
Interests: neural computing; complex networks; nonlinear functional analysis; partial differential equations; optimal control theory of differential equations; non-smooth analysis

Special Issue Information

Dear Colleagues,

This Special Issue, "Numerical and Computational Methods in Engineering, 2nd Edition", aims to explore the latest advancements and applications of numerical and computational techniques in various engineering disciplines. It provides a platform for researchers and practitioners on which to share their innovative methodologies, algorithms, and computational tools that facilitate the analysis, design, and optimization of engineering systems.

The scope of this Special Issue encompasses a broad range of engineering fields, including, but not limited to, civil engineering, mechanical engineering, electrical engineering, aerospace engineering, and chemical engineering. It welcomes contributions that address fundamental principles, the development of novel algorithms and computational techniques, the implementation of computational models, and practical applications in a diverse range of engineering domains.

Prof. Dr. Qinghe Yao
Dr. Weide Liu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • applied mathematics
  • numerical methods for partial differential equations
  • computational mechanics
  • optimization algorithms
  • structural analysis
  • heat and mass transfer simulation
  • computational electromagnetics
  • multi-physics simulations
  • computational materials science
  • high-performance computing
  • data-driven algorithms
  • big data analysis
  • machine learning in engineering

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Published Papers (1 paper)

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Research

28 pages, 80249 KB  
Article
A Variational Screened Poisson Reconstruction for Whole-Slide Stain Normalization
by Junlong Xing, Hengli Ni, Qiru Wang and Yijun Jing
Mathematics 2026, 14(8), 1373; https://doi.org/10.3390/math14081373 - 19 Apr 2026
Viewed by 329
Abstract
Stain variability in digital pathology affects both cross-center diagnostic consistency and the robustness of downstream computational analysis. In this work, we formulate stain normalization as a variational inverse problem and derive a Screened Poisson Normalization (SPN) model from the steady-state reaction–diffusion mechanism underlying [...] Read more.
Stain variability in digital pathology affects both cross-center diagnostic consistency and the robustness of downstream computational analysis. In this work, we formulate stain normalization as a variational inverse problem and derive a Screened Poisson Normalization (SPN) model from the steady-state reaction–diffusion mechanism underlying histological staining. In the CIE L*a*b* space, the model couples a gradient-domain fidelity term with a chromatic anchoring term, yielding a screened Poisson equation that preserves tissue morphology while enforcing color consistency. We prove that the corresponding variational problem is well-posed in H1(Ω) and stable with respect to perturbations of the input data. We further show that the screening term induces an intrinsic localization length 𝓁c∼λc−1/2, so that boundary perturbations decay exponentially away from tile interfaces. Based on this locality, we develop a non-overlapping tiled DCT-based spectral solver for gigapixel whole-slide images, enabling consistent tile-wise stain normalization and seamless whole-slide reassembly without heuristic boundary blending. Experiments on multi-scanner, multi-protocol, and archival-fading pathology datasets show that SPN achieves stable stain normalization with competitive chromatic alignment and strong preservation of diagnostically relevant microstructure, particularly in full-slide and tiled reconstruction settings. Supplementary experiments on synthetic pathology-like images further support the robustness of SPN under controlled color perturbations and indicate good generalization across diverse staining variations. Full article
(This article belongs to the Special Issue Numerical and Computational Methods in Engineering, 2nd Edition)
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