Related papers: Parametric shape optimization for the convected He…
In this article, we derive the asymptotic expansion, up to an arbitrary order in theory, for the solution of a two-dimensional elliptic equation with strongly anisotropic diffusion coefficients along different directions, subject to the…
Consider the wave propagation in a two-layered medium consisting of a homogeneous compressible air or fluid on top of a homogeneous isotropic elastic solid. The interface between the two layers is assumed to be an unbounded rough surface.…
We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with approximating spaces made of products of low order VEM functions and plane waves. We restrict ourselves to the 2D Helmholtz equation with impedance…
We consider the local well-posedness of the one-dimensional nonisentropic Euler equations with moving physical vacuum boundary condition. The physical vacuum singularity requires the sound speed to be scaled as the square root of the…
We established the propagation equation of acoustical wave in media with the solid/porous media cylindrical boundary and obtained the analytic solution. We suggested the boundary condition on solid-porous media cylindrical boundary. Based…
The high-frequency Helmholtz equation on the entire space is truncated into a bounded domain using the perfectly matched layer (PML) technique and subsequently, discretized by the higher-order finite element method (FEM) and the continuous…
Fundamental upper bounds are given for the plasmonic multipole absorption and scattering of a rotationally invariant dielectric sphere embedded in a lossy surrounding medium. A specialized Mie theory is developed for this purpose and when…
We consider a general compressible MHD system, where the magnetic field propagates in a heterogeneous medium. Using suitable penalization in terms of the transport coefficients we perform several singular limits. As a result we obtain: 1. A…
A generalized kinetic model equation which takes into account the frequency depence of the thermal conductivity is used to analyze the problem of sound propagation in dilute polyatomic gases. By comparing the theoretical results with some…
The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this…
A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and…
We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our analysis relies on a precise analysis of the consistency…
In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation $-\Delta u - (k^2+ {\rm i} \varepsilon)u = f$, with absorption…
The aim of this article is to prove an "almost" global existence result for some semilinear wave equations in the plane outside a bounded convex obstacle with the Neumann boundary condition.
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
We deal with the reduced four-equation model for the dynamics of heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations, and with a…
In this paper we are concerned with the initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains in spatial-temporal space. We obtain the existence of a weak…
The extended boundary condition method can be formulated to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative…
In the formulation of the problem of scattering of monochromatic waves and the numerical simulation of the solution to the Helmholtz equation, there is a computational inconvenience: the calculation is performed on a finite grid of…
We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…