Related papers: Frequency range non-Lipschitz parametric optimizat…
This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…
Quick simulations for iterative evaluations of multi-design variables and boundary conditions are essential to find the optimal acoustic conditions in building design. We propose to use the reduced basis method (RBM) for realistic room…
We establish rigorous quantitative inequalities for the first eigenvalue of the generalized $p$-Robin problem, for both the classical diffusion absorption case, where the Robin boundary parameter $\alpha$ is positive, and the…
A new simplified formula is derived for the absorption cross section of small dielectric ellipsoidal particles embedded in lossy media. The new expression leads directly to a closed form solution for the optimal conjugate match with respect…
We study thermal insulating of a bounded body $\Omega\subset \mathbb{R}^n$. Under a prescribed heat source $f\geq 0$, we consider a model of heat transfer between $\Omega$ and the environment determined by convection; this corresponds,…
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…
In a recent article, we constructed a hierarchy B_L of outer boundary conditions for Einstein's field equations with the property that, for a spherical outer boundary, it is perfectly absorbing for linearized gravitational radiation up to a…
The Jordan--Moore--Gibson--Thompson (JMGT) equation is a well-established and recently widely studied model for nonlinear acoustics (NLA). It is a third-order (in time) semilinear Partial Differential Equation (PDE) model with the…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…
In this paper, we study the nonlinear periodic Westervelt equation with excitations located within a bounded domain in $\mathbb{R}^d$, where $d \in \{2,3\}$, subject to Robin boundary conditions. This problem is of particular interest for…
We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of arbitrary shape. By introducing an artificial boundary $S$ enclosing the scatterer,…
We consider the high frequency Helmholtz equation with a variable refraction index $n^2(x)$ ($x \in \R^d$), supplemented with a given high frequency source term supported near the origin $x=0$. A small absorption parameter…
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…
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…
We present a meshless Schwarz-type non-overlapping domain decomposition method based on artificial neural networks for solving forward and inverse problems involving partial differential equations (PDEs). To ensure the consistency of…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
We prove decay estimates in the interior for solutions to elliptic equations in divergence form with Lipschitz continuous coefficients. The estimates explicitly depend on the distance from the boundary and on suitable notions of frequency…
The dynamic range is an important parameter which measures the spread of sound power, and for music signals it is a measure of recording quality. There are various descriptive measures of sound power, none of which has strong statistical…
We consider a transmission problem for the Helmholtz equation across the boundary of an extension domain. A such boundary can be Lipschitz, fractal, or of varying Hausdorff dimension for instance. We generalise the notions of layer…
In this paper, we propose a computational framework for the optimal design of broadband absorbing materials composed of plasmonic nanoparticle arrays. This design problem poses several key challenges: (1) the complex multi-particle…