相关论文: Shock capturing by anisotropic diffusion oscillati…

We provide a `user guide' to the literature of the past twenty years concerning the modeling and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit small-scale dependent shock waves. We cover several classes…

Edge preserving filters preserve the edges and its information while blurring an image. In other words they are used to smooth an image, while reducing the edge blurring effects across the edge like halos, phantom etc. They are nonlinear in…

In this paper, we consider subaperture-based approaches for the digital aberration correction (DAC) of optical coherence tomography (OCT) images. In particular, we introduce a mathematical framework for describing this class of approaches,…

Collisionless shocks are often studied in two spatial dimensions (2D), to gain insights into the 3D case. We analyze diffusive shock acceleration for an arbitrary number $N\in\mathbb{N}$ of dimensions. For a non-relativistic shock of…

Steady state simulations} of magnetized electron fluid equations with strong anisotropic diffusion based on the first-order hyperbolic approach is carried out using cell-centered higher order upwind schemes, linear and weighted essentially…

This work introduces an optimization-based $rp$-adaptive numerical method to approximate solutions of viscous, shock-dominated flows using implicit shock tracking and a high-order discontinuous Galerkin discretization on traditionally…

Real-world image super-resolution (Real-ISR) aims to reconstruct high-resolution images from low-resolution inputs degraded by complex, unknown processes. While many Stable Diffusion (SD)-based Real-ISR methods have achieved remarkable…

Numerical simulation of viscoelastic flows is challenging because of the hyperbolic nature of viscoelastic constitutive equations. Despite their superior accuracy and efficiency, pseudo-spectral methods require the introduction of…

Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a…

In this exploratory study, we apply shock-capturing schemes within the framework of the Particles on Demand kinetic model to simulate compressible flows with mild and strong shock waves and discontinuities. The model is based on the…

Limited by the encoder-decoder architecture, learning-based edge detectors usually have difficulty predicting edge maps that satisfy both correctness and crispness. With the recent success of the diffusion probabilistic model (DPM), we…

We introduce a new methodology for adding localized, space-time smooth, artificial viscosity to nonlinear systems of conservation laws which propagate shock waves, rarefactions, and contact discontinuities, which we call the $C$-method. We…

Direction of arrival (DOA) estimation employing low-resolution analog-to-digital convertors (ADCs) has emerged as a challenging and intriguing problem, particularly with the rise in popularity of large-scale arrays. The substantial…

A numerical model is proposed to simulate the adhesion, compression, and subsequent detachment of a micro-liter droplet from a superhydrophobic surface composed of chemically homogeneous pillars arranged in a periodic fashion, replicating a…

A new procedure to capture the shocks has been proposed and is demonstrated for the solutions of two-dimensional Euler equations using discontinuous Galerkin method and overset grids. A discontinuous Galerkin solver using a coarse grid…

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial…

Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods…

Denoising diffusion models have recently achieved remarkable success in image generation, capturing rich information about natural image statistics. This makes them highly promising for image reconstruction, where the goal is to recover a…

Photon transport through a diffusing slab can be described by the radiative transfer equation (RTE). When the slab is highly scattering and weakly absorbing, the RTE simplifies to the diffusion equation. In this paper, an inverse diffusion…