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We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…
Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010)…
We consider a wide variety of scattering problems including scattering by Dirichlet, Neumann, and penetrable obstacles. We consider a radial perfectly-matched layer (PML) and show that for any PML width and a steep-enough scaling angle, the…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
In this paper we present a novel extended Krylov subspace reduced-order modeling technique to efficiently simulate time- and frequency-domain wavefields in open complex structures. To simulate the extension to infinity, we use an optimal…
Spectral clustering techniques are valuable tools in signal processing and machine learning for partitioning complex data sets. The effectiveness of spectral clustering stems from constructing a non-linear embedding based on creating a…
The electromagnetic radiation of a rotating relativistic electron layers is studied numerically using particle-in-cell simulation. The results of the simulation confirm all relevant scaling properties predicted by theoretical models. These…
Diffusion problems with anisotropic features arise in the various areas of science and engineering fields. As a Lagrangian mesh-less method, SPH has a special advantage in addressing the diffusion problems due to the the benefit of dealing…
A high-order convergent and robust numerical solver is constructed and used to find complex eigenwavenumbers and electromagnetic eigenfields of dielectric objects with axial symmetry. The solver is based on Fourier--Nystr\"om discretization…
We extend the T-matrix approach to light scattering by spherical particles to some simple cases in which the scatterers are optically anisotropic. Specifically we consider cases in which the spherical particles include radially and…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…
We present a perturbative technique for modeling the scattering of light by a nonlinear material. This approach eliminates the need for an iterative algorithm to solve the fully coupled nonlinear problem. We demonstrate its effectiveness in…
In this paper we study the loss of precision of numerical methods discretizing anisotropic problems and propose alternative approaches free from this drawback. The deterioration of the accuracy is observed when the coordinates and the mesh…
We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…
We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding…
For simulation studies of (macro) molecular liquids it would be of significant interest to be able to adjust or increase the level of resolution within one region of space, while allowing for the free exchange of molecules between open…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Finite-difference (FD) modeling of seismic waves in the vicinity of dipping interfaces gives rise to artifacts. Examples are phase and amplitude errors, as well as staircase diffractions. Such errors can be reduced in two general ways. In…
This paper introduces discrete-holomorphic Perfectly Matched Layers (PMLs) specifically designed for high-order finite difference (FD) discretizations of the scalar wave equation. In contrast to standard PDE-based PMLs, the proposed method…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…