Related papers: Acoustic scattering: high frequency boundary eleme…
We consider the numerical solution of time-harmonic acoustic scattering by obstacles with uncertain geometries for Dirichlet, Neumann, impedance and transmission boundary conditions. In particular, we aim to quantify diffracted fields…
Motivated by research in metamaterials, we consider the challenging problem of acoustic wave scattering by a doubly periodic quadrant of sound-soft scatterers arranged in a square formation, which we have dubbed the quarter lattice. This…
In this paper, we present a powerful method (Atomistic Green's Function, AGF) for calculating the effective Hamiltonian of acoustic and elastic wave-scatterers. The ability to calculate the effective Hamiltonian allows for the study of…
This work is concerned with a unique combination of high order local absorbing boundary conditions (ABC) with a general curvilinear Finite Element Method (FEM) and its implementation in Isogeometric Analysis (IGA) for time-harmonic acoustic…
We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product…
We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the…
We obtain solution representation formulas for some linear initial boundary value problems posed on the half space that involve mixed spatial derivative terms via the unified transform method (UTM), also known as the Fokas method. We first…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it…
A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is computed…
Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical…
This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…
A periodizing scheme and the method of fundamental solutions are used to solve acoustic wave scattering from doubly-periodic three-dimensional multilayered media. A scattered wave in a unit cell is represented by the sum of the near and…
We describe an accelerated direct solver for the integral equations which model acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth parameterizations given on triangles, a setting which generalizes…
Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
Current theoretical treatment of mode splitting and scattering loss resulting from sub-wavelength scatterers attached to the surface of high-quality-factor whispering-gallery-mode microresonators is not satisfactory. Different models have…
Traditional finite element approaches are well-known to introduce spurious oscillations when applied to advection-dominated problems. We explore alleviation of this issue from the perspective of a generalized finite element formulation,…
Rendering highly scattering participating media using brute force path tracing is a challenge. The diffusion approximation reduces the problem to solving a simple linear partial differential equation. Flux-limited diffusion introduces…
Imaging through opaque, highly scattering walls is a long sought after capability with potential applications in a variety of fields. The use of wavefront shaping to compensate for scattering has brought a renewed interest as a potential…