数值分析

We consider in this paper the problem of computing a nonnegative low-rank approximation of the rightmost eigenpair of a linear matrix-valued real operator. We propose an algorithm based on the time integration of a suitable differential…

We introduce the TTStack sketch, a structured random projection tailored to the tensor train (TT) format that unifies existing TT-adapted sketching operators. By varying two integer parameters $P$ and $R$, TTStack interpolates between the…

For the Dirichlet integral fractional Laplacian, we prove root exponential convergence of tensor-product $hp$-finite element approximations on $(0,1)^3$, for forcing $f$ that is analytic in $[0,1]^3$. Exploiting analytic regularity…

Identifying governing partial differential equations (PDEs) from noisy spatiotemporal data remains challenging due to differentiation-induced noise amplification and ambiguity from overcomplete libraries. We propose a prior-informed…

This paper studies pressure-robustness for the axisymmetric Stokes problem. The transformation to cylindrical coordinates requires that the radially weighted velocity is divergence-free in the classical sense. Consequently, traditional…

In this paper, we propose a neural multiscale decomposition method (NeuralMD) for solving the nonlinear Klein-Gordon equation (NKGE) with a dimensionless parameter $\varepsilon\in(0,1]$ from the relativistic regime to the nonrelativistic…

A strategy to construct physics-based local surrogate models for parametric Stokes flows and coupled Stokes-Darcy systems is presented. The methodology relies on the proper generalized decomposition (PGD) method to reduce the dimensionality…

In order to numerically solve high-dimensional nonlinear PDEs and alleviate the curse of dimensionality, a stochastic particle method (SPM) has been proposed to capture the relevant feature of the solution through the adaptive evolution of…

We address the algorithmic problem of determining the reversible Markov chain $\tilde X$ that is closest to a given Markov chain $X$, with an identical stationary distribution. More specifically, $\tilde X$ is the reversible Markov chain…

We propose a unified iterative framework for the solution of frictionless mechanical contact problems, which relies exclusively on the solution of standard stiffness systems. The framework is built upon a two-step fixed-point algorithm:…

Magnetic relaxation drives plasma toward lower-energy equilibria under helicity constraints. In ideal magnetohydrodynamics (MHD), helicity is locally conserved, while resistive theories such as Taylor relaxation preserve only global…

This work presents a new design for broadband absorption of low-frequency acoustic waves using a thin coating made of subwavelength acoustic resonators arranged periodically on a reflective surface. We first study the associated scattering…

In this work, we present a mixed precision algorithm that leverages the Gram matrix and Jacobi methods to compute the singular value decomposition (SVD) of tall-and-skinny matrices. By constructing the Gram matrix in higher precision and…

Several methods for computing the action of the matrix exponential $\mathrm{e}^{\boldsymbol{A}} \boldsymbol{b}$ are expressed by substituting $\boldsymbol{A}$ into a rational approximation of the scalar exponential function. The error of…

Accurate prediction of shallow water flows relies on precise bottom topography data, yet direct bathymetric surveys are expensive and time-consuming. In contrast, remote sensing platforms such as radar or satellite altimetry provide…

Model-based reconstruction approaches for the medical imaging modality Magnetic Particle Imaging (MPI) are typically based on the Langevin model, which assumes instantaneous alignment of the particles magnetic momenta with the applied…

This paper presents a class of structure-preserving numerical methods for quantum optimal control problems, based on commutator-free Cayley integrators. Starting from the Krotov framework, we reformulate the forward and backward propagation…

We investigate a mixed finite element method for the spatial discretization of a time-fractional Allen--Cahn equation defined on a convex polyhedral domain, combined with a nonuniform Alikhanov scheme for the temporal approximation. Under…

Meshless methods are often used in numerical simulations of systems of partial differential equations (PDEs), particularly those which involve complex geometries or free surfaces. Here we present a novel compact scheme based on the local…

The starting point of this paper is that a spectral method is essentially a combination of an orthonormal basis of the underlying Hilbert space with Galerkin conditions. The choice of an orthonormal basis depends on a number of desirable…