Related papers: Numerical geometric acoustics: an eikonal-based ap…
We investigate reduced-order models for acoustic and electromagnetic wave problems in parametrically defined domains. The parameter-to-solution maps are approximated following the so-called Galerkin POD-NN method, which combines the…
In this paper we construct a parametrix for the fractional Helmholtz equation $((-\Delta)^s - \tau^{2s} r(x)^{2s} + q(x))u=0$ making use of geometrical optics solutions. We show that the associated eikonal equation is the same as in the…
The paper presents an ab initio account of the paraxial complex geometrical optics (CGO) in application to a scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough to fulfil the Sommerfeld radiation condition. By strategically truncating the computational domain with a…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial…
We propose a high-order discontinuous Galerkin scheme for nonlinear acoustic waves on polytopic meshes. To model sound propagation with and without losses, we use Westervelt's nonlinear wave equation with and without strong damping.…
We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled…
In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched…
We address the challenge of sound propagation simulations in 3D virtual rooms with moving sources, which have applications in virtual/augmented reality, game audio, and spatial computing. Solutions to the wave equation can describe wave…
Analytical methods are fundamental in studying acoustics problems. One of the important tools is the Wiener-Hopf method, which can be used to solve many canonical problems with sharp transitions in boundary conditions on a plane/plate.…
Efficient numerical solution of the acoustic Helmholtz equation in heterogeneous media remains challenging, particularly for large-scale problems with spatially-varying density - a limitation that restricts applications in biomedical…
The problem of scattering of harmonic plane acoustic waves by fluid spheroids (prolate and oblate) is addressed from an analytical approach. Mathematically, it consists in solving the Helmholtz equation in an unbounded domain with…
Solving time-harmonic wave propagation problems in the frequency domain within heterogeneous media poses significant mathematical and computational challenges, particularly in the high-frequency regime. Among the available numerical…
The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations…
We propose and analyse a numerical method for time-harmonic acoustic scattering in $\mathbb{R}^n$, $n=2,3$, by a class of inhomogeneities (penetrable scatterers) with fractal boundary. Our method is based on a Galerkin discretisation of the…
The acoustic scattering problem is modeled by the exterior Helmholtz equation, which is challenging to solve due to both the unboundedness of the domain and the high dispersion error, known as the pollution effect. We develop high-order…