数值分析

Ultrasound Computed Tomography (USCT) constitutes a nonlinear inverse problem with inherent ill-posedness that can benefit from regularization through diffusion generative priors. However, traditional approaches for solving Helmholtz…

This paper presents a wavelet Galerkin method for solving elliptic interface problems of the form $-\nabla\cdot(a\nabla u)=f$ in $\Omega\backslash \Gamma$, where $\Gamma$ is a smooth interface within $\Omega$. Since the scalar variable…

This paper studies a regularized matrix tri-factorization \(A\approx PDQ\), where \(P\) and \(Q\) are side factors and \(D\) is a central core whose conditioning can be explicitly regularized or constrained. The formulation is a structured…

Preserving the admissible set of the ideal magnetohydrodynamics (MHD) equations is important not only for producing physically meaningful numerical solutions, but more importantly for achieving robust computations. In this paper, we develop…

This article presents an arithmetic, called superposition relaxation, for bracketing the graph of a multivariate factorable function on a compact domain between a pair of underestimating and overestimating functions that are both separable.…

In this work, we proposes a CO2-temperature network model that links multi-zone mass transport and thermal dynamics through shared latent drivers, airflow and occupancy. The thermal component is formulated as a resistance-capacitance (RC)…

We review various numerical approaches to compute transport coefficients in molecular dynamics. These approaches can be broadly classified into three groups: (i) nonequilibrium methods based on applying an external driving field to the…

For Stefan problems, characterized by moving boundaries and discontinuous coefficients due to phase changes, the inherent nonconvexity of the objective functional frequently causes optimization difficulty in randomized neural network…

This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…

We introduce an $O(M)$ algorithm for evaluating the azimuthal Fourier modes $G_{k,m}$, $m = 0, 1, ..., M$, of the three-dimensional Helmholtz Green's function with real wavenumber $k$, together with all their first- and second-order…

In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop…

We propose a low-dimensional interface reduction method for elliptic interface problems based on conservative flux reconstruction. The approach combines a fitted $P_1$ finite element discretization with a flux recovery procedure following…

The power method is one of the most fundamental tools for extracting top principal components from data through low-rank matrix approximation. Yet, when the target rank is large, the cost of matrix multiplication associated with this…

We propose a hybrid method, the Neural Enrichment Finite Element Method (NEFEM), designed for problems involving strong oscillations or interface problems with weak discontinuities. This method is based on the stable generalized finite…

In this work, the traditional third-order Active Flux advection scheme is modified by reformulating the method and introducing additional parameters. The effect of these parameters is studied, leading to schemes with improved dissipative…

A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical priors, typically encoded through the PDE operator, into a…

Standard finite element discretizations of the Richards equation may violate the discrete minimum principle, producing unphysical negative saturations. While existing bound-preserving methods typically rely on computationally expensive…

We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…

Modeling complex spatial networks with multiscale heterogeneity poses significant mathematical and computational challenges. Lacking explicit PDE discretizations and facing excessive degrees of freedom, conventional methods often become…

This paper derives a new variational equation for the linear least-squares backward error by expressing the backward error in terms of a generalized eigenvalue problem and using results from indefinite linear algebra. For problems with…