相关论文: High-order BDF convolution quadrature for subdiffu…

Diffusion model-based approaches recently achieved re-markable success in MRI reconstruction, but integration into clinical routine remains challenging due to its time-consuming convergence. This phenomenon is partic-ularly notable when…

We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order…

This paper is devoted to the investigation of the backward problem for a multi-term time-fractional diffusion equation. Backward problems for fractional diffusion equations are typically studied using regularization methods due to their…

Diffusion models excel at generating high-likelihood samples but often require alignment with downstream objectives. Existing fine-tuning methods for diffusion models significantly suffer from reward over-optimization, resulting in…

In this paper, we propose a new second-order fast finite difference scheme in time for solving the Tempered Time Fractional Advection-Dispersion Equation. Under the assumption that the solution is nonsmooth at the initial time, we…

We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite…

A diffusion model, which is formulated to produce an image using thousands of denoising steps, usually suffers from a slow inference speed. Existing acceleration algorithms simplify the sampling by skipping most steps yet exhibit…

This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…

We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic…

Higher-order ODE solvers have become a standard tool for accelerating diffusion probabilistic model (DPM) sampling, motivating the widespread view that first-order methods are inherently slower and that increasing discretization order is…

In this manuscript, we propose newly-derived exponential quadrature rules for stiff linear differential equations with time-dependent fractional sources in the form $h(t^r)$, with $0<r<1$ and $h$ a sufficiently smooth function. To construct…

Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is…

In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…

We address the numerical treatment of source terms in algebraic flux correction schemes for steady convection-diffusion-reaction (CDR) equations. The proposed algorithm constrains a continuous piecewise-linear finite element approximation…

There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method…

In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…

This paper analyzes a time-stepping discontinuous Galerkin method for modified anomalous subdiffusion problems with two time fractional derivatives of orders $ \alpha $ and $ \beta $ ($ 0 < \alpha < \beta < 1 $). The stability of this…

In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system…

We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…

A high-accuracy time discretization is discussed to numerically solve the nonlinear fractional diffusion equation forced by a space-time white noise. The main purpose of this paper is to improve the temporal convergence rate by modifying…