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This manuscript is the second in a series presenting fast direct solution techniques for solving two-dimensional wave scattering problems from quasi-periodic multilayered structures. The fast direct solvers presented in the series are for…
In this paper, we propose a $\mu$-mode integrator for computing the solution of stiff evolution equations. The integrator is based on a $d$-dimensional splitting approach and uses exact (usually precomputed) one-dimensional matrix…
Driven by the growing demand for higher spectral efficiency in wireless communications, intelligent reflecting surfaces (IRS) have attracted considerable attention for their ability to dynamically reconfigure the propagation environment.…
We introduce an adaptive structured low rank algorithm to recover MR images from their undersampled Fourier coefficients. The image is modeled as a combination of a piecewise constant component and a piecewise linear component. The Fourier…
Recently, an innovative matrix CFAR detection scheme based on information geometry, also referred to as the geometric detector, has been developed speedily and exhibits distinct advantages in several practical applications. These advantages…
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…
Large-scale floating-point matrix multiplication is a fundamental kernel in many scientific and engineering applications. Most existing work only focus on accelerating matrix multiplication on FPGA by adopting a linear systolic array. This…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
We present iterative solvers to approximate the solution of numerical schemes for stochastic Stefan problems. After briefly talking about the convergence results, we tackle the question of efficient strategies for solving the nonlinear…
Masked Autoregressive (MAR) models promise better efficiency in visual generation than autoregressive (AR) models for the ability of parallel generation, yet their acceleration potential remains constrained by the modeling complexity of…
The large-scale three-dimensional inversion of surface gravity / tensor gravity data is a very challenging numerical and practical problem, which is a highly physical memory usage, time-consuming computation and high precision for…
The full-wave simulation of complex electromagnetic surfaces such as reflectarrays and metasurfaces is a challenging problem. In this paper, we present a macromodeling approach to efficiently simulate complex electromagnetic surfaces…
Adaptive representations are increasingly indispensable for reducing the in-memory and on-disk footprints of large-scale data. Usual solutions are designed broadly along two themes: reducing data precision, e.g., through compression, or…
Densifying networks and deploying more antennas at each access point are two principal ways to boost the capacity of wireless networks. However, the complicated distributions of the signal power and the accumulated interference power,…
Fast matrix multiplication is one of the most fundamental problems in algorithm research. The exponent of the optimal time complexity of matrix multiplication is usually denoted by $\omega$. This paper discusses new ideas for improving the…
In this article, we propose a new method for calculating the mixed correlation coefficient (Pearson, polyserial and polychoric) matrix and its covariance matrix based on the GMM framework. We build moment equations for each coefficient and…
This paper describes a fast direct boundary element method for elastodynamic transmission problems in two dimensions, which can be used for analyzing elastic wave scattering by an inclusion. We develop an efficient solver based on a…
The Helmholtz equation arises in many applications, such as seismic and medical imaging. These application are characterized by the need to propagate many wavelengths through an inhomogeneous medium. The typical size of the problems in 3D…
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
Strength-of-connection algorithms play a key role in algebraic multigrid (AMG). Specifically, they determine which matrix nonzeros are classified as weak and so ignored when coarsening matrix graphs and defining interpolation sparsity…