In this paper, we develop a Taylor expansion (TE) based fast multipole method (FMM) for
low frequency 3D Helmholtz Green's function in layered media. Two forms of Taylor …

Frequency-domain wave scattering problems that arise in acoustics and electromagnetism
can be often described by the Helmholtz equation. This work presents a boundary integral …

This manuscript presents a fast direct solution technique for solving two dimensional wave
scattering problems from quasi-periodic multilayered structures. When the interface …

This article presents full-spectrum, well-conditioned, Green-function methodologies for
evaluation of scattering by general periodic structures, which remains applicable on a set of …

In this research, a framework of acoustic analysis and shape optimization, based on
isogeometric boundary element method (IGA-BEM), is proposed for three-dimensional …

A boundary integral equation method for the 3-D Helmholtz equation in multilayered media
with many quasi-periodic layers is presented. Compared with conventional quasi-periodic …

This thesis presents a full-spectrum, well-conditioned, Green-function methodology for
evaluation of scattering by general periodic structures, which remains applicable on a set of …

Scattering problems are ubiquitous in scientific and engineering applications. These
problems can often be straightforwardly modeled using relatively simple linear partial …

The thesis focuses on numerical methods for boundary integral equation (BIE) formulations
of partial differential equations (PDEs). The work contains three parts: the first two consider …