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In practical applications, lattice quantizers leverage discrete lattice points to approximate arbitrary points in the lattice. An effective lattice quantizer significantly enhances both the accuracy and efficiency of these approximations.…
We consider a simple two-dimemsional harmonic lattice with random, independent and identically distributed masses. Using the methods of stochastic homogenization, we show that solutions with long wave initial data converge in an appropriate…
The strict periodicity of pulsars is the primary source of information we have to learn about their nature and environment, it allows us to challenge general relativity and measure gravitational waves. Identifying such a periodicity from a…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
A fast two-level linearized scheme with unequal time-steps is constructed and analyzed for an initial-boundary-value problem of semilinear subdiffusion equations. The two-level fast L1 formula of the Caputo derivative is derived based on…
The abundance of infrared singularities in gauge theories due to unresolved emission of massless particles (soft and collinear) represents the main difficulty in perturbative calculations. They are typically regularized in dimensional…
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…
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 surfaces in 2D. However, due to the overlapping of…
In this paper, we obtain sharp estimates for the number of lattice points under and near the dilation of a general parabola, the former generalizing an old result of Popov. We apply Vaaler's lemma and the Erd\H{o}s-Turan inequality to…
An exact expression is derived for the $(\omega,p)=0$ thermal correlator of shear stress in SU($N_c$) lattice gauge theory. I remove a logarithmic divergence by taking a suitable linear combination of the shear correlator and the correlator…
Ewald summation is an efficient method for computing the periodic sums that appear when considering the Green's functions of Stokes flow together with periodic boundary conditions. We show how Ewald summation, and accompanying truncation…
We consider the problem of optimizing a multivariate quadratic function where each decision variable is constrained to be a complex $m$'th root of unity. Such problems have applications in signal processing, MIMO detection, and the…
A variant of the Parareal method for highly oscillatory systems of PDEs was proposed by Haut and Wingate (2014). In that work they proved superlinear conver- gence of the method in the limit of infinite time scale separation. Their coarse…
We study lattice sums $\sum \frac{1}{(\|x\|\|y\|\|x+y\|)^s}$ taken over $SL_+(2,\mathbb Z)$, i.e.\ the set of pairs $(x,y)$ of primitive lattice vectors in $\mathbb Z_{\geq 0}^2$ with $\det(x, y) = 1$. We prove convergence of these and…
In this work, we develop a fast and accurate method for the scattering of flexural-gravity waves by a thin plate of varying thickness overlying a fluid of infinite depth. This problem commonly arises in the study of sea ice and ice shelves,…
Consider the elastic scattering of a time-harmonic wave by multiple well separated rigid particles in two dimensions. To avoid using the complex Green's tensor of the elastic wave equation, we utilize the Helmholtz decomposition to convert…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in…
A rarely exploited advantage of time-domain boundary integral equations compared to their frequency counterparts is that they can be used to treat certain nonlinear problems. In this work we investigate the scattering of acoustic waves by a…
The Euler--Maclaurin (EM) summation formula is used in many theoretical studies and numerical calculations. It approximates the sum $\sum_{k=0}^{n-1} f(k)$ of values of a function $f$ by a linear combination of a corresponding integral of…