相关论文: Resolving the Gibbs phenomenon via a discontinuous…

In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier-Stokes equations. Since transformation to characteristic space is already a common approach to reduce…

Spectral projectors of second order differential operators play an important role in quantum physics and other scientific and engineering applications. In order to resolve local features and to obtain converged results, typically the number…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

We consider an initial value problem for a quadratically nonlinear inviscid Burgers-Hilbert equation that models the motion of vorticity discontinuities. We use a normal form transformation, which is implemented by means of a near-identity…

We construct and justify leading order weakly nonlinear geometric optics expansions for nonlinear hyperbolic initial value problems, including the compressible Euler equations. The technique of simultaneous Picard iteration is employed to…

Two combined methods for computing solutions of time-varying semilinear differential-algebraic equations (descriptor systems) are obtained. When constructing the methods, time-varying spectral projectors which can be found numerically are…

We consider the defocusing nonlinear Schr\"odinger equations on the two-dimensional compact Riemannian manifold without boundary or a bounded domain in $\R^2$. Our aim is to give a pedagogic and self-contained presentation on the Wick…

The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such…

We construct the fundamental solution of second order parabolic equations in non-divergence form under the assumption that the coefficients are of Dini mean oscillation in the spatial variables. We also prove that the fundamental solution…

A resonant-state expansion (RSE) for open optical systems with a general frequency dispersion of the relative permittivity, described by a finite number of simple poles, is presented. As in the non-dispersive case, the RSE of dispersive…

We deal with the regularity problem for linear, second order parabolic equations and systems in divergence form with measurable data over non-smooth domains, related to variational problems arising in the modeling of composite materials and…

This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…

Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive analytical error bounds on expectation values of system…

The computation of Gr\"obner bases is an established hard problem. By contrast with many other problems, however, there has been little investigation of whether this hardness is robust. In this paper, we frame and present results on the…

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…

We consider the defocusing nonlinear Schr{\"o}dinger equation with a gauge invariant power-like nonlinearity. We prove global dispersive estimates in a semi-classical scaling, after rescaling the solution thanks to a suitable distorsion of…

The studies of Dyson-Schwinger Equations (DSEs) provide us with insights into nonperturbative phenomenon of quantum field theory. However, DSEs are essentially an infinite set of coupled Green's functions, it's necessary to decouple parts…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix…

This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…