Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
5.4
2.3
Journals
Mathematics
Special Issues
Advancements in Application of Scientific Computing and Numerical Analysis
share announcement

Advancements in Application of Scientific Computing and Numerical Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 28 February 2027 | Viewed by 1531

Editor

Prof. Dr. Faranak Courtney-Pahlevani

E-Mail Website
Guest Editor
Department of Mathematics, The Pennsylvania State University, Abington, PA 19001, USA
Interests: computational mathematics; sensitivity equation methods; ordinary and partial differential equations; numerical analysis; scientific computing

Special Issue Information

Dear Colleagues,

This special issue is dedicated to applications in scientific computing and numerical analysis ranging from high-performance numerical algorithms to large-scale computational problems and the development of such methods utilizing ordinary and partial differential equations, optimization, linear algebra, and any mathematical technique that underlies these types of computations. The analysis of numerical methods in a diverse range of problems arising from science and engineering are among the topics covered in this issue.

In this Special Issue, we invite high-quality research papers on new advances in scientific computing and numerical analysis. We welcome contributions of original research articles as well as review articles that aim to advance computational methodologies and their applications.

Prof. Dr. Faranak Courtney-Pahlevani
Guest Editor

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-anonymized 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

  • numerical analysis
  • scientific computing
  • numerical algorithms
  • numerical methods in ODE and PDE
  • optimization
  • interpolation

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

24 pages, 979 KB  
Article
Early Prediction of Convergence Outcomes in Parameterized Root-Finding: A Feature-Based Study
by Bruno Carpentieri, Andrei Velichko, Mudassir Shams and Paola Lecca
Mathematics 2026, 14(12), 2036; https://doi.org/10.3390/math14122036 - 7 Jun 2026
Viewed by 297
Abstract
We study early prediction of convergence outcomes in parameterized root-finding problems. The analysis focuses on whether short prefixes of solver trajectories contain useful information about convergence within prescribed iteration horizons, without modifying the underlying numerical scheme. To avoid relying on profile-derived targets, we [...] Read more.
We study early prediction of convergence outcomes in parameterized root-finding problems. The analysis focuses on whether short prefixes of solver trajectories contain useful information about convergence within prescribed iteration horizons, without modifying the underlying numerical scheme. To avoid relying on profile-derived targets, we use solver-level success fractions Y20, Y50, and Y100, defined as the fractions of trajectories that satisfy the convergence criterion within 20, 50, and 100 iterations, respectively. Within this setting, we compare several families of early solver-derived features, including residual-based, step-based, and trajectory-derived quantities. We also distinguish between direct-prefix predictors, which use the first N values of a feature family, and scalar summary predictors, in which the same prefix is compressed into a single descriptor. Numerical experiments on controlled parameterized root-finding benchmarks show that simple residual- and step-based summaries provide the strongest within-base predictors among the tested feature families. In particular, mean and median log residual and log step summaries are informative even at short prefixes. More elaborate trajectory-derived descriptors, including the kNN–LLE proxy, are less effective as standalone predictors in the present experiments. The results also show that prediction difficulty depends strongly on the benchmark structure: Dataset 1 leads to near-saturated prediction performance at very short prefixes, whereas the oscillatory Dataset 2A provides a more challenging and discriminative case. In this latter setting, compact scalar summaries at N=10 can occasionally match or slightly outperform the corresponding full-prefix predictors, suggesting that scalar compression may suppress part of the transient variability present in the full-prefix representation. Cross-base transfer is substantially more difficult than within-base prediction, indicating that the observed predictive relationships are not uniformly portable across the considered benchmark problems. Overall, the study suggests that, in controlled parameterized settings of the type examined here, convergence outcomes can often be predicted from simple and computationally inexpensive early trajectory summaries. The results should be interpreted as a feature-based early convergence outcome prediction study, rather than as a general diagnostic methodology for nonlinear solvers. Full article
(This article belongs to the Special Issue Advancements in Application of Scientific Computing and Numerical Analysis)
►▼ Show Figures

Graphical abstract

16 pages, 308 KB  
Article
On the Energy Dissipation Rate of Ensemble Eddy Viscosity Models of Turbulence: Shear Flows
by William Layton
Mathematics 2026, 14(8), 1319; https://doi.org/10.3390/math14081319 - 15 Apr 2026
Viewed by 497
Abstract
Classical eddy viscosity models add a viscosity term with a turbulent viscosity coefficient developed beginning with the Kolmogorov–Prandtl parameterization. Approximations of unknown accuracy of the unknown mixing lengths and turbulent kinetic energy are typically constructed by solving associated systems of nonlinear convection–diffusion-reaction equations [...] Read more.
Classical eddy viscosity models add a viscosity term with a turbulent viscosity coefficient developed beginning with the Kolmogorov–Prandtl parameterization. Approximations of unknown accuracy of the unknown mixing lengths and turbulent kinetic energy are typically constructed by solving associated systems of nonlinear convection–diffusion-reaction equations with nonlinear boundary conditions. These often over-diffuse, so additional fixes are added such as wall laws, or different approximations are used in different regions (which must also be specified). Alternately, one can solve an ensemble of NSEs with perturbed data, compute the ensemble mean and fluctuation, and simply directly compute the turbulent viscosity parameterization. This idea is recent. From previous work it seems to be of a lower complexity and greater accuracy. It also produces parameterizations with the correct near-wall asymptotic behavior. The question then arises: Does this ensemble eddy viscosity approach over-diffuse solutions? This question is addressed herein. Full article
(This article belongs to the Special Issue Advancements in Application of Scientific Computing and Numerical Analysis)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-2
Back to TopTop