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Mathematics
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Advances in High-Performance Computing, Optimization and Simulation
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Advances in High-Performance Computing, Optimization and Simulation

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

Deadline for manuscript submissions: 20 August 2025 | Viewed by 2124

Special Issue Editors

Dr. Hao Jiang

E-Mail Website
Guest Editor
College of Computer, National University of Defense Technology, Changsha, China
Interests: numerical analysis; high-performance computing
Prof. Dr. Zhe Quan

E-Mail Website
Guest Editor
College of Computer Science and Electronic Engineering, Hunan University, Changsha, China
Interests: high-performance computing; compiler; machine learning

Special Issue Information

Dear Colleagues,

High-performance computing, optimization and simulation have led to advances in several areas of science, engineering and technology. Recent developments permit the successful completion of computationally intensive problems such as those in chemistry, physics, aerospace, energy, material, healthcare, automobile development, etc. However, further research is required for developing new algorithms, methods and models for new hardware and software architecture, since many heterogeneous many-core processors with accelerators or coprocessors are now an integral part of modern computing systems, especially supercomputers. To fulfill the increasing computing demands, strategies based on heterogeneous computing, mixed precision computing, communication-avoiding computing, etc., have been adopted.

The suggested topics include the following:

  • High-performance computing;
  • Numerical analysis;
  • Accurate computing;
  • Mixed-precision algorithm;
  • Large-scale heterogeneous computing;
  • Performance tuning;
  • Optimization;
  • Parallelization;
  • Modeling and simulation.

We also welcome papers that explore new programming models and languages appropriate for the new and emerging domains and applications of HPC.

Dr. Hao Jiang
Dr. Zhe Quan
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
  • parallel algorithms
  • quantum computations
  • error analysis
  • heterogenous computing
  • mixed precision
  • communication-avoiding computing
  • performance tuning
  • optimization
  • parallelization
  • simulation

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

Published Papers (2 papers)

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Research

19 pages, 560 KiB  
Article
Accurate Sum and Dot Product with New Instruction for High-Precision Computing on ARMv8 Processor
by Kaisen Xie, Qingfeng Lu, Hao Jiang and Hongxia Wang
Mathematics 2025, 13(2), 270; https://doi.org/10.3390/math13020270 - 15 Jan 2025
Cited by 1 | Viewed by 679
Abstract
The accumulation of rounding errors can lead to unreliable results. Therefore, accurate and efficient algorithms are required. A processor from the ARMv8 architecture has introduced new instructions for high-precision computation. We have redesigned and implemented accurate summation and the accurate dot product. The [...] Read more.
The accumulation of rounding errors can lead to unreliable results. Therefore, accurate and efficient algorithms are required. A processor from the ARMv8 architecture has introduced new instructions for high-precision computation. We have redesigned and implemented accurate summation and the accurate dot product. The number of floating-point operations has been reduced from 7n−5 and 10n−5 to 4n−2 and 7n−2, compared with the classic compensated precision algorithms. It has been proven that our accurate summation and dot algorithms’ error bounds are γn−1γncond+u and γnγn+1cond+u, where ‘cond’ denotes the condition number, γn=n·u/(1−n·u), and u denotes the relative rounding error unit. Our accurate summation and dot product achieved a 1.69× speedup and a 1.14× speedup, respectively, on a simulation platform. Numerical experiments also illustrate that, under round-towards-zero mode, our algorithms are as accurate as the classic compensated precision algorithms. Full article
(This article belongs to the Special Issue Advances in High-Performance Computing, Optimization and Simulation)
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22 pages, 689 KiB  
Article
GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations
by Nicolás Murúa, Aníbal Coronel, Alex Tello, Stefan Berres and Fernando Huancas
Mathematics 2024, 12(22), 3503; https://doi.org/10.3390/math12223503 - 9 Nov 2024
Cited by 1 | Viewed by 899
Abstract
In this paper, we consider the finite difference approximation for a one-dimensional mathematical model of heat conduction in a three-layered solid with interfacial conditions for temperature and heat flux between the layers. The finite difference scheme is unconditionally stable, convergent, and equivalent to [...] Read more.
In this paper, we consider the finite difference approximation for a one-dimensional mathematical model of heat conduction in a three-layered solid with interfacial conditions for temperature and heat flux between the layers. The finite difference scheme is unconditionally stable, convergent, and equivalent to the solution of two linear algebraic systems. We evaluate various methods for solving the involved linear systems by analyzing direct and iterative solvers, including GPU-accelerated approaches using CuPy and PyCUDA. We evaluate performance and scalability and contribute to advancing computational techniques for modeling complex physical processes accurately and efficiently. Full article
(This article belongs to the Special Issue Advances in High-Performance Computing, Optimization and Simulation)
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