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Perfectly Matched Layers (PML) has become a very common method for the numerical approximation of wave and wave-like equations on unbounded domains. This technique allows one to obtain accurate solutions while working on a finite…
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…
An isogeometric boundary element method (BEM) is presented to solve scattering problems in an isotropic homogeneous medium. We consider wave problems governed by the scalar wave equation as in acoustics and the Lam\'e-Navier equations for…
In this paper, we consider finite difference approximations of the second order wave equation. We use finite difference operators satisfying the summation-by-parts property to discretize the equation in space. Boundary conditions and grid…
In this work we establish some new estimates for layer potentials of the acoustic wave equation in the time domain, and for their associated retarded integral operators. These estimates are proven using time-domain estimates based on theory…
A symmetric boundary integral formulation for the transient scattering of acoustic waves off homogeneous and isotropic elastic obstacles is analyzed. Both the acoustic scattered field and the elastodynamic excited field are represented…
The aim of this paper is to introduce a Mapping-based Hard-constrained Physics-Informed Neural Network (MH-PINN) for efficiently and accurately solving unbounded wave problems. First, we propose a coordinate mapping technique that…
We consider time-harmonic linear elasticity equations in domains containing two-dimensional semi-infinite strips. Since for such problems there exist modes with different signs of group and phase velocity, standard perfectly matched layer…
The purpose of this work is twofold: (a) To present the theoretical formulation of a 3D acoustic propagation model based on a Boundary Element Method (BEM), which uses a half-space Green function in place of the more conventional free-space…
Morse and Ingard give a coupled system of time-harmonic equations for the temperature and pressure of an excited gas. These equations form a critical aspect of modeling trace gas sensors. Like other wave propagation problems, the…
We present a numerical method for the solution of diffusion problems in unbounded planar regions with complex geometries of absorbing and reflecting bodies. Our numerical method applies the Laplace transform to the parabolic problem,…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…
The interaction of fibers in a viscous (Stokes) fluid plays a crucial role in industrial and biological processes, such as sedimentation, rheology, transport, cell division, and locomotion. Numerical simulations generally rely on slender…
A key issue in the solution of partial differential equations via integral equation methods is the evaluation of possibly singular integrals involving the Green's function and its derivatives multiplied by simple functions over discretized…
This paper proposes a novel method to establish the wellposedness and convergence theory of the uniaxial-perfectly-matched-layer (UPML) method in solving a two-dimensional acoustic scattering problem due to a compactly supported source,…
In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in…
Our objective is to stabilise and accelerate the time-domain boundary element method (TDBEM) for the three-dimensional wave equation. To overcome the potential time instability, we considered using the Burton--Miller-type boundary integral…
We prove integrated local energy decay for the damped wave equation on stationary, asymptotically flat space-times in (1 + 3) dimensions. Local energy decay constitutes a powerful tool in the study of dispersive partial differential…
We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The truncation error is included in the exact…
Controlling waves by actively changing the material parameters of a medium enables the development of new acoustic and electrical devices. Modulating the material breaks classical properties like reciprocity and the conservation of energy,…