Related papers: Uniformly accurate multiscale time integrators for…
This paper studies the PML method for wave scattering in a half space of homogeneous medium bounded by a two-dimensional, perfectly conducting, and locally defected periodic surface, and develops a high-accuracy boundary-integral-equation…
We propose a new primal-dual homotopy smoothing algorithm for a linearly constrained convex program, where neither the primal nor the dual function has to be smooth or strongly convex. The best known iteration complexity solving such a…
High dimensional space-time data pose known computational challenges when fitting spatio-temporal models. Such data show dependence across several dimensions of space as well as in time, and can easily involve hundreds of thousands of…
In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…
Dealing with time series with missing values, including those afflicted by low quality or over-saturation, presents a significant signal processing challenge. The task of recovering these missing values, known as imputation, has led to the…
We study two fundamental optimization problems: (1) scaling a symmetric positive definite matrix by a positive diagonal matrix so that the resulting matrix has row and column sums equal to 1; and (2) minimizing a quadratic function subject…
This paper proposes a novel multiscale estimator for the integrated volatility of an Ito process, in the presence of market microstructure noise (observation error). The multiscale structure of the observed process is represented…
We prove a nearly optimal error bound on the exponential wave integrator Fourier spectral (EWI-FS) method for the logarithmic Schr\"odinger equation (LogSE) under the assumption of $H^2$-solution, which is theoretically guaranteed. Subject…
Allowing for space- and time-dependence of mass in Klein--Gordon equations resolves the problem of negative probability density and of violation of Lorenz covariance of interaction in quantum mechanics. Moreover it extends their…
Moving grids are of interest in the numerical solution of hydrodynamical problems and in numerical relativity. We show that conventional integration methods for the simple wave equation in one and more than one dimension exhibit a number of…
We present high order explicit geometric integrators to solve linear-quadratic optimal control problems and $N$-player differential games. These problems are described by a system coupled non-linear differential equations with boundary…
Effective Liouville operators of the first- and the second-order symplectic integrators are obtained for the one-dimensional harmonic-oscillator system. The operators are defined only when the time step is less than two. Absolute values of…
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…
In this contribution, we generalize the concept of \textit{optimally accurate operators} proposed and used in a series of studies on the simulation of seismic wave propagation, particularly based on Geller \& Takeuchi (1995). Although these…
Multi-antenna relays and intelligent reflecting surfaces (IRSs) have been utilized to construct favorable channels to improve the performance of wireless systems. A common feature between relay systems and IRS-aided systems is the two-hop…
We establish higher order convergence rates in periodic homogenization of fully nonlinear uniformly parabolic Cauchy problems accompanied with rapidly oscillating initial data. Such result is new even for linear problems. Here we construct…
In this paper, we propose a new algorithm for the estimation of multiple time delays (TDs). Since a TD is a fundamental spatial cue for sensor array signal processing techniques, many methods for estimating it have been studied. Most of…
In this paper, we propose, analyze, and test a new fully discrete, efficient, decoupled, stable, and practically second-order time-stepping algorithm for computing MHD ensemble flow averages under uncertainties in the initial conditions and…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions obtained from a basic…