Related papers: A high-order accurate accelerated direct solver fo…
In this paper, a higher-order time-discretization scheme is proposed, where the iterates approximate the solution of the stochastic semilinear wave equation driven by multiplicative noise with general drift and diffusion. We employ a…
Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…
A discretization scheme for variable coefficient Helmholtz problems on two-dimensional domains is presented. The scheme is based on high-order spectral approximations and is designed for problems with smooth solutions. The resulting system…
We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen's method of…
We present a new boundary integral formulation for time-harmonic wave diffraction from two-dimensional structures with many layers of arbitrary periodic shape, such as multilayer dielectric gratings in TM polarization. Our scheme is robust…
A Nystrom-based high-order (HO) discretization scheme for surface integral equations (SIEs) for analyzing the electroencephalography (EEG) forward problem is proposed in this work. We use HO surface elements and interpolation functions for…
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…
This paper discusses a fast direct solver using boundary integral equations for Helmholtz transmission problems involving multiple inclusions in two dimensions. Efficiently addressing scattering problems in the presence of numerous…
The analysis of scattering from complex objects using surface integral equations is a challenging problem. Its resolution has wide ranging applications- from crack propagation to diagnostic medicine. The two ingredients of any integral…
In this paper, we will introduce a high order numerical method to solve the scattering problems with non-periodic incident fields and (locally perturbed) periodic surfaces. For the problems we are considering, the classical methods to treat…
We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
We present superalgebraic compatible Nystr\"om discretizations for the four Helmholtz boundary operators of Calder\'{o}n's calculus on smooth closed curves in 2D. These discretizations are based on appropriate splitting of the kernels…
This paper is concerned with direct and inverse scattering by a locally perturbed infinite plane (called a locally rough surface in this paper) on which a Neumann boundary condition is imposed. A novel integral equation formulation is…
We present a high-order accurate boundary-based solver for three-dimensional (3D) frequency-domain scattering from a doubly-periodic grating of smooth axisymmetric sound-hard or transmission obstacles. We build the one-obstacle solution…
In this paper, exact solutions to the problem of acoustic scattering by elastic spherical symmetric scatterers are developed. The scatterer may consist of an arbitrary number of fluid and solid layers, and scattering with single Neumann…
Boundary integral equations and Nystrom discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weakly-singular kernel arises, in which case specialized quadratures that…
This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and…
We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules.…
The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the scattering operator for each body through a local…