Advances in Numerical Mathematics for High-Performance Computing in the Exascale Era

Dear Colleagues,

High-fidelity modeling and simulation of physical systems is a critical enabling technology required for addressing some of the most challenging problems in areas such as energy, the environment, and the development of new sustainable materials. On the other hand, new exascale capabilities promise unprecedented potential for high fidelity, high confidence, and optimal solutions to complex multiscale and multiphysics problems at the heart of new challenging problems in science and engineering.

However, the transition from current petascale computing to exascale computing will not be easy: new exascale-class machines (capable of at least 10¹⁸ floating-point operations per second) will see a massive increase in the number of computing units (into the millions) in the form of homogeneous cores or heterogeneous mixtures of multipurpose CPUs and specialized processing units. As stated in some of the documents produced in some Exascale Programs [1], "the role of applied mathematics in the exascale computing effort has not been sufficiently explored" then, to respond to the new HPC systems complexity, it is to be expected that the upcoming of the exascale computing systems will require a reconsideration of all the aspects of numerical solution of science problems, including problems mathematical formulation, their discretization and scalable solution, the development of efficient and effective numerical software.

This Special Issue aims to collect recent research results in all the above-listed aspects that will enable scientific applications to harness the potential of upcoming HPC computing systems.

[1] Dongarra, J.; Hittinger, J.; Bell, J.; Chacon, L.; Falgout, R.; Heroux, M.; Hovland, P.; Ng, E.; Webster, C.; Wild, S. Applied Mathematics Research for Exascale Computing. Technical Report of the Lawrence Livermore National Lab. (LLNL): Livermore, CA, USA, 2014; LLNL-TR-651000. https://doi.org/10.2172/1149042.

Luisa Carracciuolo
Prof. Dr. Giuliano Laccetti
Prof. Dr. Marco Lapegna
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.

• mathematical models (particle-based versus continuum representations, scale-bridging models, etc.)
• discretization algorithms (high-order discretizations, parallel-in-time discretizations, etc.)
• solution algorithms (communication avoiding algorithms, multiple-precision algorithms, resilient algorithms, etc.)
• error analysis and uncertainty quantification
• efficient and effective parallel numerical software for many cores and heterogeneous computing systems