Related papers: A boundary integral equation formulation for trans…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
In this paper, we focus on a new wave equation described wave propagation in the attenuation medium. In the first part of this paper, based on the time-domain space fractional wave equation, we formulate the frequency-domain equation named…
The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density,…
Parabolic equations on evolving domains model a multitude of applications including various industrial processes such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations…
We study the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we…
In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] to port-Hamiltonian systems describing linear wave propagation…
The "flexible boundary condition" method, introduced by Sinclair and coworkers in the 1970s, remains among the most popular methods for simulating isolated two-dimensional crystalline defects, embedded in an effectively infinite atomistic…
Consider the scattering of a time-harmonic elastic plane wave by a periodic rigid surface. The elastic wave propagation is governed by the two-dimensional Navier equation. Based on a Dirichlet-to-Neumann (DtN) map, a transparent boundary…
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…
This work describes and analyzes the domain derivative for a time-dependent acoustic scattering problem. We study the nonlinear operator that maps a sound-soft scattering object to the solution of the time-dependent wave equation evaluated…
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…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
We study the Lagrange representation of the wave equation with generalized Laplacian $\operatorname{div} T \nabla$. We allow the coefficients -- the Young modulus $T$ and the density $\rho$ -- to be $\mathrm{L}^{\infty}$ or even nonlocal…
In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a…
This study considers the stability of time domain BIEMs for the wave equation in 2D. We show that the stability of time domain BIEMs is reduced to a nonlinear eigenvalue problem related to frequency domain integral equations. We propose to…
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
In this paper we propose and analyze a Discontinuous Galerkin method for a linear parabolic problem with dynamic boundary conditions. We present the formulation and prove stability and optimal a priori error estimates for the fully discrete…
We consider spectral discretizations of hyperbolic problems on unbounded domains using Laguerre basis functions. Taking as model problem the scalar advection equation, we perform a comprehensive stability analysis that includes strong…
We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these…