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Mathematics
Special Issues
Numerical Analysis and Algorithms for High-Performance Computing
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Numerical Analysis and Algorithms for High-Performance Computing

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

Deadline for manuscript submissions: 30 September 2025 | Viewed by 700

Special Issue Editors

Dr. Shengguo Li

E-Mail Website
Guest Editor
College of Computer Science, National University of Defense Technology, Changsha, China
Interests: numerical linear algebra; parallel computing; numerical analysis; machine learning
Prof. Dr. Xiaoqiang Yue

E-Mail Website
Guest Editor
School of Mathematics and Computational Science, Xiangtan University, Xiangtan, China
Interests: parallel computing; multiple grid and region decomposition method
Dr. Xuguang Chen

E-Mail
Guest Editor
College of Computer, National University of Defense Technology, Changsha, China
Interests: parallel computing; finite element analysis; damage assessment; fast algorithm
Dr. Tiaojie Xiao

E-Mail Website
Guest Editor
College of Computer Science and Technology, National University of Defense Technology, Changsha, China
Interests: parallel computing; mathematical problems; electromagnetic numerical simulation

Special Issue Information

Dear Colleagues,

In recent years, high-performance computing has become increasingly essential in various domains, including scientific simulations, electromagnetic computation, structural mechanics, engineering, data analytics, and artificial intelligence. The development of efficient numerical methods and algorithms plays a crucial role in harnessing the full potential of modern computing architectures and achieving high computational performance.

Topics of interest for this Special Issue include, but are not limited to:

  1. Numerical methods for high-performance computing;
  2. Parallel and distributed algorithms;
  3. Optimization techniques for numerical computation;
  4. Sparse and structured linear algebra;
  5. Parallel algorithms for electromagnetic computation;
  6. Parallel algorithms for structural mechanics;
  7. Machine learning algorithms for high-performance computing;
  8. Multigrid and Domain Decomposition algorithms;
  9. Parallel-in-time (PinT) algorithms.

We invite researchers and practitioners to submit original research papers, review articles, and case studies that address the challenges and opportunities in numerical analysis and algorithms for high-performance computation. Submissions should present novel contributions, theoretical insights, experimental results, or practical applications relevant to the theme of the Special Issue.

Dr. Shengguo Li
Prof. Dr. Xiaoqiang Yue
Dr. Xuguang Chen
Dr. Tiaojie Xiao
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 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • high-performance computing (HPC)
  • numerical analysis
  • sparse matrix computations
  • direct and iterative methods
  • electromagnetic computation
  • algorithm optimization
  • structural mechanics
  • parallel-in-time
  • multigrid methods
  • domain decomposition
  • machine learning in HPC

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

Published Papers (1 paper)

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22 pages, 2191 KiB  
Review
Towards Efficient HPC: Exploring Overlap Strategies Using MPI Non-Blocking Communication
by Yuntian Zheng and Jianping Wu
Mathematics 2025, 13(11), 1848; https://doi.org/10.3390/math13111848 - 2 Jun 2025
Viewed by 170
Abstract
As high-performance computing (HPC) platforms continue to scale up, communication costs have become a critical bottleneck affecting overall application performance. An effective strategy to overcome this limitation is to overlap communication with computation. The Message Passing Interface (MPI), as the de facto standard [...] Read more.
As high-performance computing (HPC) platforms continue to scale up, communication costs have become a critical bottleneck affecting overall application performance. An effective strategy to overcome this limitation is to overlap communication with computation. The Message Passing Interface (MPI), as the de facto standard for communication in HPC, provides non-blocking communication primitives that make such overlapping feasible. By enabling asynchronous communication, non-blocking operations reduce idle time of cores caused by data transfer delays, thereby improving resource utilization. Overlapping communication with computation is particularly important for enhancing the performance of large-scale scientific applications, such as numerical simulations, climate modeling, and other data-intensive tasks. However, achieving efficient overlapping is non-trivial and depends not only on advances in hardware technologies such as Remote Direct Memory Access (RDMA), but also on well-designed and optimized MPI implementations. This paper presents a comprehensive survey on the principles of MPI non-blocking communication, the core techniques for achieving computation–communication overlap, and some representative applications in scientific computing. Alongside the survey, we include a preliminary experimental study evaluating the effectiveness of asynchronous progress mechanism on modern HPC platforms to support the development of parallel programs for HPC researchers and practitioners. Full article
(This article belongs to the Special Issue Numerical Analysis and Algorithms for High-Performance Computing)
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