58 citations · 95 across the 23 of their papers we have counts for
24 papers
Directional Tangency and Anomalous Far-Field Decay for Schr{ö}dinger Equations
Ruming Zhang
We identify a directional tangency mechanism responsible for anomalous far-field decay in Schrödinger equations. For constant-coefficient operators, we introduce a directional deco…
Sliced Spectral Analysis and Geometric Mechanisms of Radiation for Periodic Elliptic Operators
Ruming Zhang
Radiation in higher-dimensional periodic media is fundamentally more difficult than in one dimension because the multidimensional spectral parameterization no longer admits the one…
The PML-Method for a Scattering Problem for a Local Perturbation of an Open Periodic Waveguide
Andreas Kirsch, Ruming Zhang
The perfectly matched layers method is a well known truncation technique for its efficiency and convenience in numerical implementations of wave scattering problems in unbounded do…
Does PML exponentially absorb outgoing waves scattering from a periodic surface?
Wangtao Lu, Kuanrong Shen, Ruming Zhang
The PML method is well-known for its exponential convergence rate and easy implementation for scattering problems with unbounded domains. For rough-surface scattering problems, aut…
Higher order convergence of perfectly matched layers in 3D bi-periodic surface scattering problems
Ruming Zhang
The perfectly matched layer (PML) is a very popular tool in the truncation of wave scattering in unbounded domains. In Chandler-Wilde & Monk et al. 2009, the author proposed a conj…
Fast convergent PML method for scattering with periodic surfaces: the exceptional case
Ruming Zhang
In the author's previous paper (Zhang et al. 2022), exponential convergence was proved for the perfectly matched layers (PML) approximation of scattering problems with periodic sur…
A spectral decomposition method to approximate DtN maps in complicated waveguides
Ruming Zhang
In this paper, we propose a new spectral decomposition method to simulate waves propagating in complicated waveguides. For the numerical solutions of waveguide scattering problems,…
A nonuniform mesh method for wave scattered by periodic surfaces
Tilo Arens, Ruming Zhang
In this paper, we propose a new nonuniform mesh method to simulate acoustic scattering problems in two dimensional periodic structures with non-periodic incident fields numerically…
Exponential convergence of perfectly matched layers for scattering problems with periodic surfaces
Ruming Zhang
The main task in this paper is to prove that the perfectly matched layers (PML) method converges exponentially with respect to the PML parameter, for scattering problems with perio…
High order complex contour discretization methods to simulate scattering problems in locally perturbed periodic waveguides
Ruming Zhang
In this paper, two high order complex contour discretization methods are proposed to simulate wave propagation in locally perturbed periodic closed waveguides. As is well known the…
Numerical method for scattering problems in periodic waveguides
Ruming Zhang
In this paper, we propose a new numerical method for scattering problems in periodic waveguide, based on the newly established contour integral representation of solutions in a pre…
Spectrum decomposition of translation operators in periodic waveguide
Ruming Zhang
Scattering problems in periodic waveguides are interesting but also challenging topics in mathematics, both theoretically and numerically. Due to the existence of eigenvalues, the…
Near-field imaging of locally perturbed periodic surfaces
Xiaoli Liu, Ruming Zhang
This paper concerns the inverse scattering problem to reconstruct a locally perturbed periodic surface. Different from scattering problems with quasi-periodic incident fields and p…
Scattering problems from slightly perturbed periodic surfaces: Part II. High order numerical method
Ruming Zhang
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Base…
Scattering problems from slightly perturbed periodic surfaces: Part I. regularity of the Bloch transformed fields
Ruming Zhang
Rough surface scattering problems are always very challenging both theoretically and numerically. In this paper, we adopt the Bloch transform and the perturbation theory to investi…
A Bloch transform based numerical method for the rough surface scattering problems
Ruming Zhang
In this paper, we will study the Bloch transformed rough surface scattering problems, and propose a numerical method based on the Bloch transformed problems. Based on the mathemati…
Numerical Methods for Quasi-Periodic Incident Fields Scattered by Locally Perturbed Periodic Surfaces
Ruming Zhang
Waves scattering from unbounded structures are always complicated problems for numerical simulations. For the case that the non-periodic incident field scattered by (locally pertur…
An FFT-based algorithm for efficient computation of Green's functions for the Helmholtz and Maxwell's equations in periodic domains
Bo Zhang, Ruming Zhang
The integral equation method is widely used in numerical simulations of 2D/3D acoustic and electromagnetic scattering problems, which needs a large number of values of the Green's…
Reconstruction of Local Perturbations in Periodic Surfaces
Armin Lechleiter, Ruming Zhang
This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered fiel…
A High Order Numerical Method for Scattering from Locally Perturbed Periodic Surfaces
Ruming Zhang
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…
The Study of the Bloch Transformed Fields Scattered by Locally Perturbed Periodic Surfaces
Ruming Zhang
Scattering problems with locally perturbed periodic surfaces have been studied both theoretically and numerically in recent years. In this paper, we will discuss the regularity res…
A Floquet-Bloch transform based numerical method for scattering from locally perturbed periodic surfaces
Armin Lechleiter, Ruming Zhang
Scattering problems for periodic structures have been studied a lot in the past few years. A main idea for numerical solution methods is to reduce such problems to one periodicity…
A Convergent Numerical Scheme for Scattering of Aperiodic Waves from Periodic Surfaces Based on the Floquet-Bloch Transform
Armin Lechleiter, Ruming Zhang
Periodic surface structures are nowadays standard building blocks of optical devices. If such structures are illuminated by aperiodic time-harmonic incident waves as, e.g., Gaussia…
Recursive integral method for transmission eigenvalues
Ruihao Huang, Allan A. Struthers, Jiguang Sun +1
Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous med…