相关论文: Linear-in-Complexity Computational Strategies for …

We consider regularized approximate cloaking for the Helmholtz equation. Various cloaking schemes have been recently proposed and extensively investigated. The existing cloaking schemes in literature are (optimally) within $|\ln\rho|^{-1}$…

We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…

In this work, we develop a numerical homogenization approach for the fully nonlinear Landau-Lifshitz equation with rough coefficients, including non-periodicity and nonseparable scales. Direct numerical resolution of such multiscale…

Implicit particle-in-cell codes offer advantages over their explicit counterparts in that they suffer weaker stability constraints on the need to resolve the higher frequency modes of the system. This feature may prove particularly valuable…

Since its first demonstration in 1995, terahertz time-domain imaging has attracted an increasingly growing interest for its ability to reveal spectral fingerprints of materials, probe changes in refractive index and absorption, as well as…

We present a novel coarse-to-fine framework that derives a semi-regular multiscale mesh representation of an original input mesh via remeshing. Our approach differs from the conventional mesh wavelet transform strategy in two ways. First,…

A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…

We proposed a novel dense line spectrum super-resolution algorithm, the DMRA, that leverages dynamical multi-resolution of atoms technique to address the limitation of traditional compressed sensing methods when handling dense point-source…

We provide a mathematical analysis of and a numerical framework for full-field optical coherence elastography, which has unique features including micron-scale resolution, real-time processing, and non-invasive imaging. We develop a novel…

An accurate treatment of electronic spectra in large systems with a technique such as time dependent density functional theory (TDDFT) is computationally challenging. Due to the Nyquist sampling theorem, direct real time simulations must be…

Deep learning models have been successfully used in computer vision and many other fields. We propose an unorthodox algorithm for performing quantization of the model parameters. In contrast with popular quantization schemes based on…

In this paper, we propose a novel machine learning method based on an adaptive tensor neural network subspace for solving quasiperiodic elliptic problems. To this end, we first provide a theoretical analysis of the associated quasiperiodic…

Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…

Terahertz computed tomography (THz CT) has drawn significant attention because of its unique capability to bring multi-dimensional object information from invisible to visible. However, current physics-model-based THz CT modalities present…

Metasurfaces represent a new frontier in materials science paving for unprecedented methods of controlling electromagnetic waves, with a range of applications spanning from sensing to imaging and communications. For pulsed terahertz…

We study a simple nonlinear model defined on the honeycomb and triangular lattices. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable…

Terahertz (THz) communications open a new frontier for the wireless network thanks to their dramatically wider available bandwidth compared to the current micro-wave and forthcoming millimeter-wave communications. However, due to the short…

Plasmonic metamaterials and metasurfaces offer new opportunities in developing high performance terahertz emitters and detectors beyond the limitations of conventional nonlinear materials. However, simple meta-atoms for second-order…

Terahertz microscopy has attracted attention owing to distinctive characteristics of the THz frequency region, particularly non-ionizing photon energy, spectral fingerprint, and transparency to most nonpolar materials. Nevertheless, the…

We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…