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A new, very fast method for 3D radiative transfer on fully threaded grids with arbitrarily high angular resolution is presented. The method uses completely cell-based discretization, and is ideally suited for problems with diffuse…
Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the…
We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical…
We propose an energy-stable parametric finite element method (ES-PFEM) to discretize the motion of a closed curve under surface diffusion with an anisotropic surface energy $\gamma(\theta)$ -- anisotropic surface diffusion -- in two…
The rapid advancement of diffusion models has significantly improved high-quality image generation, making generated content increasingly challenging to distinguish from real images and raising concerns about potential misuse. In this…
Multirate digital signal processing and model reduction applications require computation of the frequency truncated norm of a discrete-time system. This paper explains how to compute the frequency truncated norm of a discrete-time system.…
'The spectral leakage from windowing and the picket fence effect from discretization' have been among the standard contents in textbooks for many decades. The spectral leakage and picket fence effect would cause the distortions in…
Due to distribution shift, deep learning based methods for image dehazing suffer from performance degradation when applied to real-world hazy images. In this paper, we consider a dehazing framework based on conditional diffusion models for…
Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…
Fast-Fourier Transform (FFT) methods have been widely used in solid mechanics to address complex homogenization problems. However, current FFT-based methods face challenges that limit their applicability to intricate material models or…
Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This…
The average spectrum method is a promising approach for the analytic continuation of imaginary time or frequency data to the real axis. It determines the analytic continuation of noisy data from a functional average over all admissible…
Wave propagation and scattering problems in acoustics are often solved with boundary element methods. They lead to a discretization matrix that is typically dense and large: its size and condition number grow with increasing frequency. Yet,…
In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…
The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…
Optical super-resolution has been widely employed to beat spatial diffraction limit, which is often stated by Abbe-Rayleigh criterion. Analogously, we propose a frequency super-resolution method, which beats conventional spectral resolution…
Previous low-light image enhancement (LLIE) approaches, while employing frequency decomposition techniques to address the intertwined challenges of low frequency (e.g., illumination recovery) and high frequency (e.g., noise reduction),…
An asymptotic-preserving (AP) implicit-explicit PN numerical scheme is proposed for the gray model of the radiative transfer equation, where the first- and second-order numerical schemes are discussed for both the linear and nonlinear…
Speckle noise severely limits the quality of images acquired from coherent imaging systems such as Synthetic Aperture Radar (SAR) and medical ultrasound. Traditional second-order PDE-based despeckling approaches, although popular, often…