Advanced Finite Element Methods for Wave Applications

Dear Colleagues,

Deterministic numerical modelling of wave propagation is of a great interest for many applications. However, such modelling has always been a major challenge, especially when considering higher frequencies, i.e., large wavenumbers. In general, numerical methods capture an approximate wavelength, which leads to the accumulation of large errors when the domain spans many thousands or even millions of wavelengths. Furthermore, modelling large domains, especially in three dimensions, can easily produce millions of degrees of freedom, hence producing massive linear systems to be solved that are also ill-conditioned. Moreover, waves often propagate to infinity. This also may require some approximations to enable modelling infinite domains.

In the past two decades, several breakthroughs have been achieved in modelling waves. The developed techniques enabled modelling the wave phenomenon on a scale that can be a game-changing factor for multiple applications. In this Special Issue, we aim to create a collection of the recent developments in relation to such techniques. Although we focus on finite element methods, contributions relating to other methods are also welcome. Contributions based on different aspects of wave modelling such as linear solvers, preconditioners, meshing techniques, high order approximations, boundary conditions and high-performance computing all remain relevant. Finally, the issue covers different applications of waves in acoustics, electromagnetism, optics, hydrodynamics and elasticity.

Prof. Dr. M. Shadi Mohamed
Prof. Dr. Amane Takei
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. Applied Sciences 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 2400 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.

• High order finite element methods
• Spectral Element Methods
• Isogeometric Analysis
• Enriched finite element method
• Acoustic waves
• Elastic waves
• Electromagnetic waves
• Helmholtz equation
• Wave equation