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Recent advances in Fourier-based computational approaches for PDEs

The use of Fourier analysis for frequency domain representation or high-order trigonometric interpolation can be found in a plethora of applications throughout science and engineering, including those related to surface representation, scattered data approximation, signal processing, and differential equations. In particular, Fourier-based methods for solving high-resolution discretized problems (e.g., those governed by PDEs) in solid and fluid mechanics have enjoyed particular interest due to the relatively low computational complexity and memory requirements involved in computing fast Fourier transforms (FFTs). Indeed, by reducing convolution and differentiation operations to simple products in the frequency domain (which can be easily obtained by means of the FFT), fast and accurate numerical methods (including recently-introduced neural network operators) can be developed to treat a variety of initial and/or boundary value problems for the mathematical modeling of mechanical behavior (e.g., wave propagation and dynamics, diffusion, material homogenization, etc.). However, widespread use for such applications has been hindered in no small part by the well-known difficulties of Fourier analysis in handling complex physical boundary conditions, complicated domains, discontinuities/irregularities, non-uniformly spaced data, and, more commonly, non-periodicity (i.e., Gibb’s phenomenon).

In the spirit of addressing such challenges and facilitating broader applicability, this special issue aims to highlight recent contributions from applied mathematicians and computational mechanicians on the general development of Fourier-based approaches toward solving problems in acoustics, solids, or fluids.

Topics of particular interest include, but are not limited to:

• Modified/non-standard Fourier series representations
• FFT-based numerical methods for PDEs
• Fourier-based machine learning techniques

Guest Editors

Faisal Amlani (Lead Guest Editor), LMPS, Université Paris-Saclay, France
Niema M. Pahlevan, University of Southern California, USA 
Carlos Pérez-Arancibia, University of Twente, Netherlands

Peer Review Process

Advanced Modeling and Simulation in Engineering Sciences operates a single-blind peer-review system, where the reviewers are aware of the names and affiliations of the authors, but the reviewer reports provided to authors are anonymous.

Submitted manuscripts will generally be reviewed by two to three experts who will be asked to evaluate whether the manuscript is scientifically sound and coherent, whether it duplicates already published work, and whether or not the manuscript is sufficiently clear for publication. The Editors will reach a decision based on these reports and, where necessary, they will consult with members of the Editorial Board.

Articles will undergo the journal’s standard peer-review process and are subject to all of the journal’s standard policies, including those pertaining to Collections. Articles will be added to the Collection as they are published.

Submission Instructions

Before submitting your manuscript, please ensure you have carefully read the submission guidelines for Advanced Modeling and Simulation in Engineering Sciences. Your complete manuscript should be submitted through the Advanced Modeling and Simulation in Engineering Sciences submission system, selecting inclusion with the thematic series, “Physics Informed Machine Learning” when prompted. All submissions will undergo rigorous peer review and accepted articles will be published within the journal as a collection.

Open Access Publication

Submissions will also benefit from the usual advantages of open access publication:Rapid publication: Online submission, electronic peer review and production make the process of publishing your article simple and efficient.
High visibility and international readership in your field: Open access publication ensures high visibility and maximum exposure for your work - anyone with online access can read your article.
No space constraints: Publishing online means unlimited space for figures, extensive data and video footage.
Authors retain copyright, licensing the article under a Creative Commons license: articles can be freely redistributed and reused as long as the article is correctly attributed.

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