Related papers: The Complex-Scaled Half-Space Matching Method
In this paper we consider the classic problems of scattering of waves from perfectly conducting cylinders with piecewise smooth boundaries. The scattering problems are formulated as integral equations and solved using a Nystr\"om scheme…
The perfectly matched layers (PMLs), as a boundary termination over an unbounded spatial domain, are widely used in numerical simulations of wave propagation problems. Given a set of discretization parameters, a procedure to select the PML…
The main purpose of this project is to develop a new active set method (ASM) called a working set method (WSM) for solving a general nonlinear inequality constrained minimization problem in a Hilber space. Mathematical analysis is carried…
We consider the numerical solution of the scattering of time-harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium, in two dimensions. Boundary integral formulations…
Feature matching between image pairs is a fundamental problem in computer vision that drives many applications, such as SLAM. Recently, semi-dense matching approaches have achieved substantial performance enhancements and established a…
This paper further develops the Method of Matched Sections (MMS), a robust numerical framework for the solution of boundary value problems governed by partial differential equations. It demonstrates its unique applicability to the…
Complex Semi-Definite Programming (SDP) is introduced as a novel approach to phase retrieval enabled control of monochromatic light transmission through highly scattering media. In a simple optical setup, a spatial light modulator is used…
In this paper, we study error diffusion techniques for digital halftoning from the perspective of 1-bit Sigma-Delta quantization. We introduce a method to generate Sigma-Delta schemes for two-dimensional signals as a weighted combination of…
Matching promises transparent causal inferences for observational data, making it an intuitive approach for many applications. In practice, however, standard matching methods often perform poorly compared to modern approaches such as…
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer…
The design of absorbing boundary conditions (ABC) in a numerical simulation is a challenging task. In the best cases, spurious reflections remain for some angles of incidence or at certain wave lengths. In the worst, ABC are not even…
In this paper, we introduce Holographic Spectral Multiplexing (HSM) as a novel technique to enable multiple-input multiple-output (MIMO) communication in optical networks. HSM uses the spectral space of ultrashort laser pulses to create…
Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is of great challenge. A useful approach, the projection method…
In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our…
Helium atom scattering (HAS) is a well established technique for examining the surface structure and dynamics of materials at atomic sized resolution. The HAS technique Helium spin-echo spectroscopy opens up the possibility of compressing…
In this paper we consider the numerical solution of the Hamiltonian wave equation in two spatial dimension. We use the Mimetic Finite Difference (MFD) method to approximate the continuous problem combined with a symplectic integration in…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
We introduce COLOSS, a program designed to address the scattering problem using a bound-state technique known as complex scaling. In this method, the oscillatory boundary conditions of the wave function are transformed into exponentially…
In this paper, we present a fast boundary integral method accelerated by the fast multipole method (FMM) for acoustic wave scattering governed by the scalar Helmholtz equation in multi-layered two-dimensional media. Multiple scatterers are…
We introduce harmonization, an ensembling method that combines several "noisy" decoders to generate highly accurate decoding predictions. Harmonized ensembles of MWPM-based decoders achieve lower logical error rates than their individual…