数值分析

This paper considers large-scale nonsymmetric continuous-time algebraic Riccati equations (NAREs) that admit low-rank solutions. Low-rank alternating direction implicit (ADI) methods have proven to be an efficient approach for solving…

High-order partial differential equations (PDEs) require derivative regularity that standard $C^0$ finite element infrastructures do not directly provide on unstructured meshes. We propose a mesh-intrinsic generalized finite element method…

We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursive algorithm for computing rank one tensor completion. This…

Higham's conjecture on the growth factor of complex symmetric positive definite matrices is a longstanding problem in the stability theory of Gaussian elimination without pivoting. It asserts that every complex matrix $A=B+iC$ with $B$ and…

This work presents an analytical and computational study of fractional-order delay differential equations formulated using both the conformable and Caputo derivatives. For the conformable case, we develop the associated integral,…

Recently a new approach to analyze and create algebraic multigrid methods (AMG) for nonsymmetric and indefinite matrices was established. Convergence is measured in general norms induced by a certain HPD matrix $B$ and $B$-orthogonal…

Algebraic Multigrid (AMG) methods have been proven to be effective solvers for large-scale linear algebraic systems $Ax = b$ with Hermitian positive definite (HPD) matrix $A$. For such problems the convergence in the $A$-norm is well…

Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computers. Solving ordinary and partial differential equations (PDEs) is essential in simulations. However, existing…

We propose new formulations of geometric curvature flows -- referred to as \emph{dual formulations} -- that are equivalent to the original formulations but provide a novel framework for constructing linearly implicit and energy-stable…

We introduce a variational dictionary learning algorithm with hybrid penalization for single-cell microscopy signals. The cost functional couples least-squares data fidelity with total-variation (TV) regularization and a non-negativity…

This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we…

We propose one finite element method for both second order linear uniformly elliptic PDE in non-divergence form and the uniformly elliptic Hamilton-Jacobi-Bellman (HJB) equation. For both linear elliptic PDE in non-divergence form and the…

We present a numerical method for simulating rarefied gases that interact with moving boundaries and rigid bodies. The gas is described by the BGK equation in Lagrangian form and solved using an Arbitrary Lagrangian-Eulerian method, in…

This paper develops a robust solver for the Maxwell eigenproblem in 3D photonic crystals with anisotropic media. The solver employs the kernel compensation technique under the framework of Yee's scheme to eliminate null space and enable…

Complex physical systems which exhibit fluid-like behavior are often modeled as non-Newtonian fluids. A crucial element of a non-Newtonian model is the rheology, which relates inner stresses with strain-rates. We propose a framework for…

In this paper, we investigate the correlated diffusion of two ion species governed by a Poisson-Nernst-Planck (PNP) system. Here we further validate the numerical scheme recently proposed in \cite{astuto2025asymptotic}, where a time…

In this paper, we propose and validate a two-species Multiscale model for a Poisson-Nernst-Planck (PNP) system, focusing on the correlated motion of positive and negative ions under the influence of a trap. Specifically, we aim to model…

We propose a novel framework for solving nonlinear PDEs using sparse radial basis function (RBF) networks. Sparsity-promoting regularization is employed to prevent over-parameterization and reduce redundant features. This work is motivated…

We consider the approximation of minimal geodesics between two closed sets in $\mathbb{R}^D$ endowed with a smooth Riemannian metric. The continuous problem is formulated as the minimization of the energy functional over piecewise smooth…

Tree tensor networks (TTNs) provide a compact and structured representation of high-dimensional data, making them valuable in various areas of computational mathematics and physics. In this paper, we present a rigorous mathematical…