Mathematical Methods in Parallel Computing and High-Performance Computing

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 30 April 2026 | Viewed by 793

Special Issue Editor


E-Mail Website
Guest Editor
National Key Laboratory of Parallel and Distributed Computing, National University of Defense Technology, Changsha 410073, China
Interests: computer vision; deep learning; computational learning; GPU; FPGA; high-performance computing; software radio

Special Issue Information

Dear Colleagues,

This Special Issue, entitled "Mathematical Method in Parallel Computing and High-Performance Computing", aims to explore the latest advancements in mathematical techniques that enhance the efficiency and scalability of parallel and high-performance computing (HPC) systems. This Special Issue seeks to bring together researchers and practitioners to discuss innovative algorithms, numerical methods, and theoretical frameworks that address the challenges of large-scale data processing and complex computational tasks. The focus will be on how mathematical approaches can optimize performance, reduce computational time, and improve the accuracy of simulations in various scientific and engineering domains. The goal is to foster interdisciplinary collaboration and promote the development of robust, scalable, and efficient computational methods for the next generation of HPC systems.

Dr. Rongchun Li
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-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

  • parallel computing
  • high-performance computing (HPC)
  • mathematical algorithms
  • numerical methods
  • scalability
  • computational efficiency
  • data processing
  • scientific simulations
  • interdisciplinary collaboration
  • computational optimization

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 (1 paper)

Order results
Result details
Select all
Export citation of selected articles as:

Research

26 pages, 13449 KB  
Article
Pipelined Space-Time Krylov Method with Preconditioning: A Parallel-in-Time Algorithm for Biot’s Quasi-Static Poroelasticity
by Guoliang Ju, Xin Xia, Zeyuan Zhou, Yan Gao, Huipeng Gu, Jiake Tian, Longfeng Nie, Xucong Wang and Wei Xing
Mathematics 2026, 14(7), 1177; https://doi.org/10.3390/math14071177 - 1 Apr 2026
Viewed by 227
Abstract
This paper presents a preconditioner-based parallel-in-time (PinT) method for solving the quasi-static Biot’s consolidation model in poroelasticity, a problem characterized by stiff coupling and saddle-point structures. To address the computational challenges of the resulting large-scale linear systems, we design two physics-based Schur-complement approximation [...] Read more.
This paper presents a preconditioner-based parallel-in-time (PinT) method for solving the quasi-static Biot’s consolidation model in poroelasticity, a problem characterized by stiff coupling and saddle-point structures. To address the computational challenges of the resulting large-scale linear systems, we design two physics-based Schur-complement approximation preconditioners that ensure robust Krylov convergence. Crucially, the method achieves a pipelined space-time architecture by introducing an inverted time-stepping mechanism: Instead of sequential time marching, time steps are traversed in the inner loop, while the outer loop applies an iterative solve across the entire space-time trajectory. This structure relaxes the strict dependency on fully converged solutions at each time step, enabling approximate solutions to be iteratively refined in parallel. Implemented as a pipelined wavefront scheme with strictly nearest-neighbor communication, the algorithm achieves strong scalability. Algorithmic verification conducted on systems with up to 200 thousand degrees of freedom demonstrates stable convergence and sustained strong scaling with up to 128 cores. The proposed approach maintains the accuracy of the underlying finite element discretization while alleviating the “time bottleneck,” making it highly effective for large-scale, long-duration poroelastic simulations. Full article
Show Figures

Figure 1

Back to TopTop