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Analytical Methods in Wave Scattering and Diffraction, 3rd Edition
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Analytical Methods in Wave Scattering and Diffraction, 3rd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 1 January 2027 | Viewed by 2039

Special Issue Editor

Prof. Dr. Nikolaos L. Tsitsas

E-Mail Website
Guest Editor
School of Informatics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Interests: applied mathematics; wave propagation and scattering theory; partial differential equations; integral equations; mathematical modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Boundary-value problems (BVPs) pertaining to scattering and radiation by devices supporting novel wave phenomena are of primary importance in Applied and Computational Mathematics, Computational Physics and Engineering. Modeling such BVPs with analytical or semi-analytical techniques is essential to obtain solutions with controllable accuracy and in small execution time. These solutions can be considered as significant benchmarks and starting points for optimizing efficiently the devices parameters in order to achieve specific near- or far-field variations. The purpose of this special issue is to gather contributions from experts on analytical and semi-analytical techniques with application domains including but not limited to single- or multiple-particle scattering, metamaterials, direct and inverse scattering by inclusions in layered media, propagation in waveguides, resonators, and analysis of periodic, layered or complex media. The techniques applied for the analytical modeling are expected to span from integral-equation/differential-equation based methodologies to generalized separation of variables and Fourier-series expansions as well as to Galerkin and eigenfunction series techniques. Contributions with main emphasis on numerical methods for wave phenomena are also welcome provided that they exploit analytical means at certain stages of the procedures employed for the derivations of the solutions.

Prof. Dr. Nikolaos L. Tsitsas
Guest Editor

Manuscript Submission Information

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Keywords

  • waves
  • scattering
  • diffraction
  • radiation
  • integral equation techniques
  • asymptotic analysis
  • metamaterials and periodic structures
  • electromagnetics
  • photonics
  • acoustic waves
  • elastic waves

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Related Special Issue

Published Papers (3 papers)

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Research

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21 pages, 2253 KB  
Article
Feedback-Controlled Manipulation of Multiple Defect Bands of Phononic Crystals with Segmented Piezoelectric Sensor–Actuator Array
by Soo-Ho Jo
Mathematics 2026, 14(2), 361; https://doi.org/10.3390/math14020361 - 21 Jan 2026
Viewed by 441
Abstract
Defect modes in phononic crystals (PnCs) provide strongly localized resonances that are essential for frequency-dependent wave filtering and highly sensitive sensing. Their functionality increases greatly when their spectral characteristics can be externally tuned without altering the structural configuration. However, existing feedback control strategies [...] Read more.
Defect modes in phononic crystals (PnCs) provide strongly localized resonances that are essential for frequency-dependent wave filtering and highly sensitive sensing. Their functionality increases greatly when their spectral characteristics can be externally tuned without altering the structural configuration. However, existing feedback control strategies rely on laminated piezoelectric defects, which have uniform electromechanical loading that causes voltage cancellation for even-symmetric defect modes. Consequently, only odd-symmetric defect bands can be manipulated effectively, which limits multi-band tunability. To overcome this constraint, we propose a segmented piezoelectric sensor–actuator design that enables symmetry-dependent feedback at the defect site. We develop a transfer-matrix analytical framework to incorporate complex-valued feedback gains directly into dispersion and transmission calculations. Analytical predictions demonstrate that real-valued feedback yields opposite stiffness modifications for odd- and even-symmetric modes. This enables the simultaneous tuning of both defect bands and induces an exceptional-point-like coalescence. In contrast, imaginary feedback preserves stiffness but modulates effective damping, generating a parity-dependent amplification-suppression response. The analytical results closely match those of fully coupled finite-element simulations, reducing computation time by more than two orders of magnitude. These findings demonstrate that segmentation-enabled feedback provides an efficient and scalable approach to tunable, multi-band, non-Hermitian wave control in piezoelectric PnCs. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction, 3rd Edition)
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10 pages, 467 KB  
Article
Local Splitting into Incoming and Outgoing Waves and the Integral Representation of Regular Scalar Waves
by Didier Felbacq and Emmanuel Rousseau
Mathematics 2025, 13(17), 2875; https://doi.org/10.3390/math13172875 - 5 Sep 2025
Viewed by 891
Abstract
The problem of the integral representation over a bounded surface of a regular field satisfying the Helmholtz equation in all space is investigated. This problem is equivalent to local splitting into an incoming field and an outgoing field. This splitting is not possible [...] Read more.
The problem of the integral representation over a bounded surface of a regular field satisfying the Helmholtz equation in all space is investigated. This problem is equivalent to local splitting into an incoming field and an outgoing field. This splitting is not possible in general. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction, 3rd Edition)
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Review

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17 pages, 709 KB  
Review
A Review of Inverse Scattering Imaging Methods Based on Transmission Eigenfunctions
by Youzi He
Mathematics 2026, 14(10), 1586; https://doi.org/10.3390/math14101586 - 7 May 2026
Viewed by 137
Abstract
Designing imaging methods is one of the important issues in inverse scattering problems. In recent years, some studies have shown that the transmission eigenfunctions contain important qualitative and quantitative information about the unknown scatterers. These spectral properties are closely related to the intrinsic [...] Read more.
Designing imaging methods is one of the important issues in inverse scattering problems. In recent years, some studies have shown that the transmission eigenfunctions contain important qualitative and quantitative information about the unknown scatterers. These spectral properties are closely related to the intrinsic nature of the scatterers and provide a connection between the scattering data and the geometry and the material characteristics of the target objects. This paper reviews recent developments in inverse scattering imaging methods that utilize local and global geometric structures of the transmission eigenfunctions. We first summarize the theoretical properties of these eigenfunctions, and then discuss the imaging algorithms based on them. Particular emphasis is placed on the theoretical justification of these imaging methods, including comparisons between them and traditional qualitative reconstruction methods. Finally, we discuss the current challenges and open problems, such as issues related to the theoretical explanation of super-resolution effect, limited-aperture data, and the extension to more complex physical models. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction, 3rd Edition)
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