Related papers: A frequency-dependent $p$-adaptive technique for s…
A simple analytical model is developed to analyze and explain the complex dynamics of the multi-peak modulation instability spectrum observed in dispersion oscillating optical fibers [M. Droques et al., 37, 4832-4834 Opt. Lett., (2012)]. We…
Shape derivative is an important analytical tool for studying scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape…
This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining…
Non-Gaussian statistics are a challenge for data assimilation. Linear methods oversimplify the problem, yet fully nonlinear methods are often too expensive to use in practice. The best solution usually lies between these extremes.…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
This work introduces a time-adaptive strategy that uses a refinement estimator based on the first Frenet curvature. In dynamics, a time-adaptive strategy is a mechanism that interactively proposes changes to the time step used in iterative…
In this paper we describe an adaptive Levin method for numerically evaluating integrals of the form $\int_\Omega f(\mathbf x) \exp(i g(\mathbf x)) \,d\Omega$ over general domains that have been meshed by transfinite elements. On each…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
The attention towards food products characteristics, such as nutritional properties and traceability, has risen substantially in the recent years. Consequently, we are witnessing an increased demand for the development of modern tools to…
The problem of designing adaptive stepsize sequences for the gradient descent method applied to convex and locally smooth functions is studied. We take an adaptive control perspective and design update rules for the stepsize that make use…
In high dispersion spectra of rotating bodies such as stars and planets, the rotation contributes significantly to, and sometimes dominates, the line broadening. We present a simple method for rotationally broadening large wavelength ranges…
In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr\"odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the so-called bond order…
This article investigates adaptive mesh refinement procedures for the time-domain wave equation with Neumann boundary conditions, formulated as an equivalent hypersingular boundary integral equation. Space-adaptive and time-adaptive…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…
We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which…
This paper presents a novel, efficient, high-order accurate, and stable spectral element-based model for computing the complete three-dimensional linear radiation and diffraction problem for floating offshore structures. We present a…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
We present a numerical approach to the solution of elastic phonon scattering problems based on a frequency domain decomposition of the atomistic equations of motion and the use of perfectly matched layer or PML boundaries. Unlike MD…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…