Related papers: Overlapping Schwarz methods are not anisotropy-rob…
In this article, we prove the global well-posedness and scattering of the cubic focusing infinite coupled nonlinear Schr\"odinger system on $\mathbb{R}^2$ below the threshold in $L_x^2h^1(\mathbb{R}^2\times \mathbb{Z})$. We first establish…
Interactive global illumination remains a challenge in radiometrically- and geometrically-complex scenes. Specialized sampling strategies are effective for specular and near-specular transport because the scattering has relatively low…
In this note we take a new look at the local convergence of alternating optimization methods for low-rank matrices and tensors. Our abstract interpretation as sequential optimization on moving subspaces yields insightful reformulations of…
While solving Partial Differential Equations (PDEs) with finite element methods (FEM), serendipity elements allow us to obtain the same order of accuracy as rectangular tensor-product elements with many fewer degrees of freedom (DOFs). To…
We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…
We study the scattering behavior of global solutions to stochastic nonlinear Schr\"odinger equations with linear multiplicative noise. In the case where the quadratic variation of the noise is globally finite and the nonlinearity is…
The linearly constrained convex composite programming problems whose objective function contains two blocks with each block being the form of nonsmooth+smooth arises frequently in multiple fields of applications. If both of the smooth terms…
The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the scattering operator for each body through a local…
A numerical method for solving the equations modeling acoustic scattering is presented. The method is capable of handling several dozen scatterers, each of which is several wave-lengths long, on a personal work station. Even for geometries…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
In this paper we study the loss of precision of numerical methods discretizing anisotropic problems and propose alternative approaches free from this drawback. The deterioration of the accuracy is observed when the coordinates and the mesh…
We investigate the scattering of light by a nonlinear, anisotropic slab under conical incidence and arbitrary polarization, within the framework of Maxwell's equations, where the nonlinearities are described by nonlinear susceptibility…
Pattern formation induced by wrinkling is a very common phenomenon exhibited in soft-matter substrates. In all these systems wrinkles develop in presence of compressively stressed thin films lying on compliant substrates. Here we…
We are interested in the scattering problem for the cubic 3D nonlinear defocusing Schr\"odinger equation with variable coefficients. Previous scattering results for such problems address only the cases with constant coefficients or assume…
In this paper, we focus on the two-dimensional surface quasi-geostrophic equation with fractional horizontal dissipation and fractional vertical thermal diffusion. On the one hand, when the dissipation powers are restricted to a suitable…
We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform "rigid body" rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter…
A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple…
This is the second paper in a series on light scattering from optically anisotropic scatterers embedded in an isotropic medium. The apparently complex T-matrix theory involving mixing of angular momentum components turns out to be an…
Granular materials such as sand, powders, and grains are omnipresent in daily life, industrial applications, and earth-science [1]. When unperturbed, they form stable structures that resemble the ones of other amorphous solids like metallic…
In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…