相关论文: On the stability of robust dynamical low-rank appr…

Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction…

Fractional Ginzburg-Landau equations as the generalization of the classical one have been used to describe various physical phenomena. In this paper, we propose a numerical integration method for solving space fractional Ginzburg-Landau…

In this paper, we present a new adaptive rank approximation technique for computing solutions to the high-dimensional linear kinetic transport equation. The approach we propose is based on a macro-micro decomposition of the kinetic model in…

We consider the minimum-energy control of a car, which is modelled as a point mass sliding on the ground in a fixed direction, and so it can be mathematically described as the double integrator. The control variable, representing the…

Dynamical low-rank approximation, as has been demonstrated recently, can be extremely efficient in solving kinetic equations. However, a major deficiency is that they do not preserve the structure of the underlying physical problem. For…

In this article we study the numerical approximation of incompressible miscible displacement problems with a linearised Crank-Nicolson time discretisation, combined with a mixed finite element and discontinuous Galerkin method. At the heart…

The Vlasov--Maxwell equations are used for the kinetic description of magnetized plasmas. As they are posed in an up to 3+3 dimensional phase space, solving this problem is extremely expensive from a computational point of view. In this…

The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and…

Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…

Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…

The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…

Dynamical low-rank algorithms are a class of numerical methods that compute low-rank approximations of dynamical systems. This is accomplished by projecting the dynamics onto a low-dimensional manifold and writing the solution directly in…

Low-rank methods for kinetic equations have attracted increasing attention due to their effectiveness in reducing the high dimensionality of phase space. In our previous work [G. Wang & J. Hu, J. Comput. Phys. 558 (2026) 114884], we…

Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…

The efficient numerical integration of large-scale matrix differential equations is a topical problem in numerical analysis and of great importance in many applications. Standard numerical methods applied to such problems require an unduly…

We proposed a novel dense line spectrum super-resolution algorithm, the DMRA, that leverages dynamical multi-resolution of atoms technique to address the limitation of traditional compressed sensing methods when handling dense point-source…

We propose a numerical integrator for determining low-rank approximations to solutions of large-scale matrix differential equations. The considered differential equations are semilinear and stiff. Our method consists of first splitting the…

This paper presents a rank-adaptive implicit-explicit integrator for the tensor approximation of three-dimensional convection-diffusion equations. In particular, the recently developed Reduced Augmentation Implicit Low-rank (RAIL)…

One of the most effective orthogonal moments, discrete Racah polynomials (DRPs) and their moments are used in many disciplines of sciences, including image processing, and computer vision. Moments are the projections of a signal on the…

The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…