journal: Journal of Numerical Mathematics

Impact Factor: 3.8

Published since March 1, 2001

Journal of Numerical Mathematics

ISSN: 1569-3953

Editor-in-Chief: Maxim Olshanskiy

Managing Editor: Andrea Bonito

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About this journal

Objective
The Journal of Numerical Mathematics (formerly East-West Journal of Numerical Mathematics) contains high-quality papers featuring contemporary research in all areas of Numerical Mathematics. This includes the development, analysis, and implementation of new and innovative methods in Numerical Linear Algebra, Numerical Analysis, Optimal Control/Optimization, and Scientific Computing. The journal will also publish applications-oriented papers with significant mathematical content in computational fluid dynamics and other areas of computational engineering, finance, and life sciences.

Topics

Numerical Mathematics
Computational Mathematics
Applied Mathematics
Numerical Linear Algebra
Numerical Analysis
Optimal Control/Optimization
Scientific Computing
Computational Fluid Dynamics
Finance
Life Sciences

Article formats
Original research articles

Information on Submission Process

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Your benefits

Pioneering research on all aspects of Numerical Mathematics
Internationally recognized reviewers and editorial board
Practical applications of researches

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Supplementary Materials

Topics

Volume 32 (2024)

Volume 31 (2023)

Volume 30 (2022)

Volume 29 (2021)

Volume 28 (2020)

Volume 27 (2019)

Volume 26 (2018)

Volume 25 (2017)

Volume 24 (2016)

Volume 23 (2015)

Volume 22 (2014)

Volume 21 (2013)

Volume 20 (2012)

Volume 19 (2011)

Volume 18 (2010)

Volume 17 (2009)

Volume 16 (2008)

Volume 15 (2007)

Volume 14 (2006)

Volume 13 (2005)

Volume 12 (2004)

Volume 11 (2003)

Volume 10 (2002)

Volume 9 (2001)

Journal Impact Factor	3.8	2023, Journal Citation Reports (Clarivate, 2024)
5-year Journal Impact Factor	3.0	2023, Journal Citation Reports (Clarivate, 2024)
Journal Citation Indicator	2.41	2023, Journal Citation Reports (Clarivate, 2024)
CiteScore	5.9	2023, Scopus (Elsevier B.V., 2024)
SCImago Journal Rank	1.892	2023, SJR (Scimago Lab, 2024; Data Source: Scopus)
Source Normalized Impact per Paper	2.237	2023, CWTS Journal Indicators (CWTS B.V., 2024; Data Source: Scopus)
Mathematical Citation Quotient	1.75

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Increasing Impact Factor
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Top scholars and reviewers
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Submission process

Submit your article via our Online Submission Tool following our Instructions for Authors
The authors can provide the names and e-mail addresses of up to four potential reviewers
The decision on the acceptance is taken after a peer-reviewing procedure
Each article must begin with an abstract of less than 150 words. The abstract must be followed by an appropriate classification according to MSC 2010 (Mathematics Subject Classification) and a list of 3 to 6 keywords. The short title for the running head should contain at most 80 characters, spaces inclusive
Authors are asked to follow a few basic guidelines while formatting their paper for publication, in order for the journal to be as homogeneous in appearance as possible. Please download the LaTeX class file and the respective sample file including the instructions for formatting here
The affiliation, postal and electronic addresses of all authors should be placed at the very end of the paper
Figures must be of sufficiently high resolution (minimum 600 dpi). Lettering of all figures within the article should be uniform in style (preferably a sans serif typeface like Helvetica) and of sufficient size (ca. 8 pt.). Uppercase letters A, B, C, etc. should be used to identify parts of multi-part figures. Cite all figures in the text in numerical order. Indicate the approximate placement of each figure. Do not embed figures within the text body of the manuscript; submit figures in separate files. In a TEX document EPS files may be incorporated into the TEX file by using one of the standard macro packages
Provide a short descriptive title and a legend to make each figure self-explanatory. Explain all symbols used in the figures. Remember to use the same abbreviations as in the text body
Authors are encouraged to submit illustrations in color if necessary for their scientific content
References should be collected at the end of the paper, numbered with Arabic numerals in alphabetical order of the authors' names and surrounded by square brackets. Please use abbreviations for titles of journals in accordance with those listed in Mathematical Reviews.
o Articles in journals:　
[1] A. Carbonaro, G. Metafune and C. Spina, Parabolic Schrödinger operators, J. Math
Anal. and Appl. 343 (2008), 965-974.
o Articles ahead of print:　
[2] D. Farley and L. Sabalka, Presentations of graph braid groups, Forum Math. (2010), doi: 10.1515/FORM.2011.086.
o Books and Monographs:　
[3] I. M. Isaacs, Character theory of finite groups, AMS Chelsea Publishing, 2006.
o Chapters:　
[4] T. De Medts, F. Haot, R. Knop and H. Van Maldeghem, On the uniqueness of the unipotent subgroups of some Moufang sets, in: Finite Geometries, Groups, and Computation, pp. 43-66, de Gruyter, Berlin, 2006.

Galley proofs will be sent to all authors in due time with a request to carefully check them
After publication each author will receive a PDF file of the final version for private use only.

Please note

Contributions submitted to this journal must be written in clear and concise English
Only unpublished material can be accepted, and authors may not republish their paper in the same or similar form
Before submitting your article please have a look at our Ethical Guidelines and our Copyright Transfer Agreement
Once your article is accepted you have the option to publish it open access
Our Repository Policy allows you to distribute 30 PDF copies of your published article to colleagues (the PDF has to include the information that it is an author's copy). Please also feel free to distribute the link to the online abstract
If you have any general questions please visit our FAQ page for authors

We look forward to receiving your manuscript!

Hybrid Open Access

In this journal, authors have the option to publish their article under an open access license. Open Access allows you as an author to retain copyright and share your findings with colleagues and interested parties worldwide without any restraints.
Please note that authors from institutions with which we have a transformative agreement can publish open access without paying an article processing charge (APC). More information on the eligible institutions and articles can be found under the "Funding and Support" tab here.

Editorial

Editor-in-Chief
Maxim Olshanskii, Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA
molshan@math.uh.edu

Managing Editor
Andrea Bonito, Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
bonito@math.tamu.edu

Editorial Advisory Board

Markus Bachmayr, Institut für Geometrie und Praktische Mathematik
Michele Benzi, Scuola Normale Superiore di Pisa
Susanne Brenner, Louisiana State University
Erik Burman, University College London
Carsten Carstensen, Humboldt University of Berlin
Miloslav Feistauer, Charles University in Prague
Simon Foucart, Texas A&M University
Jean-Luc Guermond, Texas A&M University
Johnny Guzman, Brown University
Daniel Kressner, EPFL
Christoph Lehrenfeld, University of Gottingen
Frédéric Nataf, Sorbonne University
Michael Neilan, University of Pittsburgh
Fabio Nobile, EPFL
Alfio Quarteroni, Politecnico di Milan
Leo Rebholz, Clemson University
Sergey Repin, Russian Academy of Science
Arnold Reusken, RWTH Aachen University
Valeria Simoncini, University of Bologna
Martin Stoll, TU Chemnitz
Eugene Tyrtyshnikov, Russian Academy of Science
Stefan Volkwein, University of Konstanz
Shawn Walker, Louisiana State University
Jun Zou, The Chinese University of Hong Kong

Honorary Members
Raytcho Lazarov, Texas A&M University
Pekka Neittaanmäki, University of Jyväskylä
Olivier Pironneau, French Academy of Sciences
Rolf Rannacher, Heidelberg University

Volume 33 Issue 1

March 2025

Publicly Available February 28, 2025

Frontmatter

Page range: i-iii

Download PDF

October 7, 2024

Stabilized weighted reduced order methods for parametrized advection-dominated optimal control problems governed by partial differential equations with random inputs

Fabio Zoccolan, Maria Strazzullo, Gianluigi Rozza

Page range: 1-35

Abstract

In this work, we analyze Parametrized Advection-Dominated distributed Optimal Control Problems with random inputs in a Reduced Order Model (ROM) context. All the simulations are initially based on a finite element method (FEM) discretization; moreover, a space-time approach is considered when dealing with unsteady cases. To overcome numerical instabilities that can occur in the optimality system for high values of the Péclet number, we consider a Streamline Upwind Petrov–Galerkin technique applied in an optimize-then-discretize approach. We combine this method with the ROM framework in order to consider two possibilities of stabilization: Offline-Only stabilization and Offline-Online stabilization. Moreover we consider random parameters and we use a weighted Proper Orthogonal Decomposition algorithm in a partitioned approach to deal with the issue of uncertainty quantification. Several quadrature techniques are used to derive weighted ROMs: tensor rules, isotropic sparse grids, Monte-Carlo and quasi Monte-Carlo methods. We compare all the approaches analyzing relative errors between the FEM and ROM solutions and the computational efficiency based on the speedup-index.

November 5, 2024

Augmenting the grad-div stabilization for Taylor–Hood finite elements with a vorticity stabilization

Volker John, Christian Merdon, Marwa Zainelabdeen

Page range: 37-54

Abstract

The least squares vorticity stabilization (LSVS), proposed in N. Ahmed, G. R. Barrenechea, E. Burman, J. Guzmán, A. Linke, and C. Merdon (“A pressure-robust discretization of Oseen’s equation using stabilization in the vorticity equation,” SIAM J. Numer. Anal. , vol. 59, no. 5, pp. 2746–2774, 2021) for the Scott–Vogelius finite element discretization of the Oseen equations, is studied as an augmentation of the popular grad-div stabilized Taylor–Hood pair of spaces. An error analysis is presented which exploits the situation that the velocity spaces of Scott–Vogelius and Taylor–Hood are identical. Convection-robust error bounds are derived under the assumption that the Scott–Vogelius discretization is well posed on the considered grid. Numerical studies support the analytic results and they show that the LSVS-grad-div method might lead to notable error reductions compared with the standard grad-div method.

Open Access October 7, 2024

Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated

Todd Dupont, Johnny Guzmán, L. Ridgway Scott

Page range: 55-86

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Abstract

Inspired by the methods developed in J. H. Bramble, T. Dupont, and V. Thomée (“Projection methods for Dirichlet’s problem in approximating polygonal domains with boundary-value corrections,” Math. Comput. , vol. 26, no. 120, pp. 869–879, 1972), we introduce a new technique that yields a symmetric formulation and has similar performance. The new method is based on a Robin-type problem on an approximate polygonal domain. Optimal error estimates in the energy norm are proved for piecewise quadratics and cubics. We provide numerical experiments that show our theoretical results are sharp.

March 30, 2024

Optimal evaluation of symmetry-adapted n-correlations via recursive contraction of sparse symmetric tensors

Illia Kaliuzhnyi, Christoph Ortner

Page range: 87-104

Abstract

We present a comprehensive analysis of an algorithm for evaluating high-dimensional polynomials that are invariant (or equi-variant) under permutations and rotations. This task arises in the evaluation of linear models as well as equivariant neural network models of many-particle systems. The theoretical bottleneck is the contraction of a high-dimensional symmetric and sparse tensor with a specific sparsity pattern that is directly related to the symmetries imposed on the polynomial. The sparsity of this tensor makes it challenging to construct a highly efficient evaluation scheme. Bachmayr et al. (“Polynomial approximation of symmetric functions,” Math. Comp. , vol. 93, pp. 811–839, 2024) and Lysogorskiy et al. (“Performant implementation of the atomic cluster expansion (pace): application to copper and silicon,” npj Comput. Mater. , vol. 7, Art. no. 97, 2021) introduced a recursive evaluation strategy that relied on a number of heuristics, but performed well in tests. In the present work, we propose an explicit construction of such a recursive evaluation strategy and show that it is in fact optimal in the limit of infinite polynomial degree.

(Deutsch)

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Online ISSN: 1569-3953
Print ISSN: 1570-2820
Type: Journal
Language: English
Publisher: De Gruyter
First published: March 1, 2001
Publication Frequency: 4 issues per year
Audience: Researchers and practitioners of all disciplines related to Numerical Mathematics

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Journal of Numerical Mathematics

Frontmatter

Stabilized weighted reduced order methods for parametrized advection-dominated optimal control problems governed by partial differential equations with random inputs

Abstract

Augmenting the grad-div stabilization for Taylor–Hood finite elements with a vorticity stabilization

Abstract

Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated

Abstract

Optimal evaluation of symmetry-adapted n-correlations via recursive contraction of sparse symmetric tensors

Abstract

Augmenting the grad-div stabilization for Taylor–Hood finite elements with a vorticity stabilization