Related papers: Accelerated 3D Maxwell Integral Equation Solver us…
A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounded half-space or an infinitely extended layer, Sommerfeld and…
In this paper, we present a fast multipole method (FMM) for solving the two-dimensional Laplace equation in a half-plane with Robin boundary conditions. The method is based on a novel expansion theory for the reaction component of the…
We present a fast direct solution method for the advection-diffusion equation in one and two dimensions with non-periodic boundaries. Computational cost is reduced to $\mathcal O(N)$ by making a low-rank approximation of the Green's…
This paper presents a new strategy to deal with the excessive diffusion that standard finite volume methods for compressible Euler equations display in the limit of low Mach number. The strategy can be understood as using centered…
An efficient surface integral equation-based method is proposed for the analysis of electromagnetic scattering from multilayered media containing complex periodic inclusions. The proposed method defines equivalent currents at the interfaces…
In this paper, two formulations for the computation of the dyadic Green's functions of Maxwell's equations in layered media are presented in details. The first formulation derived using TE/TM decomposition is well-known and intensively used…
We introduce and analyze various Regularized Combined Field Integral Equations (CFIER) formulations of time-harmonic Navier equations in media with piece-wise constant material properties. These formulations can be derived systematically…
The electromagnetic behavior of plasmonic structures can be predicted after discretizing and solving a linear system of equations, derived from a continuous surface integral equation (SIE) and the appropriate boundary conditions, using a…
We present a high-order boundary integral equation (BIE) method for the frequency-domain acoustic scattering of a point source by a singly-periodic, infinite, corrugated boundary. We apply it to the accurate numerical study of acoustic…
This paper addresses the inverse scattering problem for Maxwell's equations. We first show that a bianisotropic scatterer can be uniquely determined from multi-static far-field data through the factorization analysis of the far-field…
Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…
Empirical Green's functions (EGFs) extracted from seismic ambient noise have been widely used to image Earth's interior structures, and the resolution of EGF-based tomography depends on the spatial density of seismic stations. However, due…
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 interaction of fibers in a viscous (Stokes) fluid plays a crucial role in industrial and biological processes, such as sedimentation, rheology, transport, cell division, and locomotion. Numerical simulations generally rely on slender…
We present an efficient way to solve the Bethe-Salpeter equation (BSE), a model for the computation of absorption spectra in molecules and solids that includes electron-hole excitations. Standard approaches to construct and diagonalize the…
High-order methods gain more and more attention in computational fluid dynamics. However, the potential advantage of these methods depends critically on the availability of efficient elliptic solvers. With spectral-element methods, static…
A surface integral equation solver is proposed for fast and accurate simulation of interconnects embedded in stratified media. A novel technique for efficient computation of the multilayer Green's function is proposed. Using the Taylor…
The Marchenko method is a powerful tool for reconstructing full-wavefield Green's functions using surface-recorded seismic data. These Green's functions can then be utilized to produce subsurface images that are not affected by artifacts…
The Immersed Boundary (IB) method of Peskin (J. Comput. Phys., 1977) is useful for problems involving fluid-structure interactions or complex geometries. By making use of a regular grid that is independent of the geometry, the IB framework…
In this paper we introduce a new fix point iteration scheme for solving nonlinear electromagnetic scattering problems. The method is based on a spectral formulation of Maxwell's equations called the Bidirectional Pulse Propagation…