Related papers: A spectral boundary element method for acoustic in…
This text proposes a fast, rapidly convergent Nystr\"{o}m method for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by inhomogeneous obstacles, while…
A spectral formulation of the boundary integral equation method for antiplane problems is presented. The boundary integral equation method relates the slip and the shear stress at an interface between two half-planes. It involves evaluating…
We propose a new finite element method for Helmholtz equation in the situation where an acoustically permeable interface is embedded in the computational domain. A variant of Nitsche's method, different from the standard one, weakly…
This article discusses the well-posedness and error analysis of the coupling of finite and boundary elements for transmission or contact problems in nonlinear elasticity. It concerns W^{1,p}-monotone Hencky materials with an unbounded…
We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth, strictly convex obstacles with Neumann boundary conditions. Using integral equation…
This paper proposes a Cartesian grid-based boundary integral method for efficiently and stably solving two representative moving interface problems, the Hele-Shaw flow and the Stefan problem. Elliptic and parabolic partial differential…
We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…
The quantum behavior of charge carriers in semiconductor structures is often described in terms of the effective mass Schr\"{o}dinger equation, neglecting the rapid fluctuations of the wave function on the scale of the atomic lattice. For…
We describe and analyze a quasi-Trefftz DG method for solving boundary value problems for the homogeneous diffusion-advection-reaction equation with piecewise-smooth coefficients. Trefftz schemes are high-order Galerkin methods whose…
We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise…
This article presents and analyzes a $p^{th}$-degree immersed finite element (IFE) method for elliptic interface problems with nonhomogeneous jump conditions. In this method, jump conditions are approximated optimally by basic IFE and…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…
Sound-soft fractal screens can scatter acoustic waves even when they have zero surface measure. To solve such scattering problems we make what appears to be the first application of the boundary element method (BEM) where each BEM basis…
This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…
This paper presents a new fast multipole boundary element method (FM-BEM) for solving the acoustic transmission problems in 2D periodic media. We divide the periodic media into many fundamental blocks, and then construct the boundary…
We study a symmetric BEM-FEM coupling scheme for the scattering of transient acoustic waves by bounded inhomogeneous anisotropic obstacles in a homogeneous field. An incident wave in free space interacts with the obstacles and produces a…
This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose…
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, new boundary differential equations for the two-dimensional exterior scattering problem have been derived. It has been shown that the Helmholtz equation can be reduced to an inhomogeneous Bessel's equation in a body-fitted…
We consider the efficient numerical solution of the three-dimensional wave equation with Neumann boundary conditions via time-domain boundary integral equations. A space-time Galerkin method with $C^\infty$-smooth, compactly supported basis…