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We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave…
In a time-harmonic setting, we show for heterogeneous acoustic and homogeneous electromagnetic wavesguides stability estimates with the stability constant depending linearly on the length $L$ of the waveguide. These stability estimates are…
The point symmetry group is studied for the generalized Webster-type equation describing non-linear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the admitted…
We propose and analyze a space-time finite element method for Westervelt's quasilinear model of ultrasound waves in second-order formulation. The method combines conforming finite element spatial discretizations with a…
The dispersion curves of (elastic) waveguides frequently exhibit crossings and osculations (also known as veering, repulsion, or avoided crossing). Osculations are regions in the dispersion diagram where curves approach each other…
Three kinds of Fragile Points Methods based on Petrov-Galerkin weak-forms (PG-FPMs) are proposed for analyzing heat conduction problems in nonhomogeneous anisotropic media. This is a follow-up of the previous study on the original FPM based…
We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…
We generalize earlier solutions of gravitational shocks sourced by distributional null stress-energy and analyze their observable effects. A systematic method is proposed to demonstrate consistency between the gravitational effects of a…
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for elasticity interface problems on general polygonal and polyhedral meshes, without requiring convexity constraints. The method utilizes bubble functions as…
The elastic behavior of materials is of critical importance for the design, fabrication, and testing of industrial and structural components. The ease with which the wave angle of incidence can be varied makes ultrasonic techniques well…
We consider a time-harmonic wave problem, appearing for example in water-waves and in acoustics, in a setting such that the analysis reduces to the study of a 2D waveguide problem with a Neumann boundary condition. The geometry is symmetric…
In this paper, we study the numerical solution of an elastic/viscoelastic wave equation with non smooth wave speed and internal localized distributed Kelvin-Voigt damping acting faraway from the boundary. Our method is based on the Finite…
This paper is the second part of a work devoted to the modelling of thin elastic plates with small, periodically distributed piezoelectric inclusions. We consider the equations of linear elasticity coupled with the electrostatic equation,…
Polarisation-maintaining ZBLAN optical fibres with small elliptical cores are attractive for nonlinear frequency conversion, for example in supercontinuum generation (SCG), and for dispersion management in ultrafast fibre laser systems…
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…
Electro-momentum coupling in piezoelectric metamaterials with broken inversion symmetry enables asymmetric elastic wave transport by linking macroscopic electric fields to momentum, an effect analogous to Willis coupling in elastic media. A…
Birefringence phase-matching based \c{hi}(2) ZnGeP2 (ZGP) waveguide platform has been recently reported for excellent mid-infrared laser generation. Here, a detailed theoretical characterization of mode transmission taking waveguide…
Unoriented surface reconstructions based on the Gauss formula have attracted much attention due to their elegant mathematical formulation and excellent performance. However, the isotropic characteristics of the formulation limit their…
This paper proposes an efficient boundary-integral based "windowed Green function" methodology (WGF) for the numerical solution of three-dimensional electromagnetic problems containing dielectric waveguides. The approach, which generalizes…
A numerical method to calculate equilibrium vortex-line configurations in bulk anisotropic type-II superconductors, at zero temperature, placed in an external magnetic field is introduced and applied to two physical problems. The method is…