数值分析
Recently, triple decomposition has attracted increasing attention for decomposing third-order tensors into three factor tensors. However, this approach is limited to third-order tensors and enforces uniformity in the lower dimensions across…
Meshless collocation with multiquadric radial basis functions (MQ-RBFs) delivers high accuracy for the three-dimensional Helmholtz equation but produces dense, severely ill-conditioned linear systems. We develop and evaluate three…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…
The nonlinear (preconditioned) conjugate gradient N(P)CG method and the locally optimal (preconditioned) minimal residual LO(P)MR method, both of which are used for the iterative computation of sparse approximate inverses (SPAIs) of…
Due to its nonlinearity, bi-harmonic dissipation, and backward heat-like term in the absence of a divergence-free condition, the $2$-D/$3$-D Kuramoto-Sivashinsky equation poses significant challenges for both mathematical analysis and…
This paper presents a unified analytical framework for a two phase underwater wireless optical communication (UWOC) system that integrates Simultaneous Lightwave Information and Power Transfer (SLIPT) using a photovoltaic (PV) panel…
The convergence analysis of a third-order scheme for the highly nonlinear Landau-Lifshitz-Gilbert equation with a non-convex constraint is considered. In this paper, we first present a fully discrete semi-implicit method for solving the…
This work develops polynomial-degree-robust (p-robust) equilibrated a posteriori error estimates for $H(\rm curl)$, $H(\rm div)$ and $H(\rm divdiv)$ problems, based on $H^1$ auxiliary space decomposition. The proposed framework employs…
This paper presents compact, symmetric, and high-order finite difference methods (FDMs) for the variable Poisson equation on a $d$-dimensional hypercube. Our scheme produces a symmetric linear system: an important property that does not…
We propose a localized consensus-based method for sampling from non-Gaussian distributions. This method arises from an alternative derivation of consensus-based sampling (CBS). Starting from ensemble-preconditioned Langevin dynamics, we…
Zero-dimensional (0D) cardiovascular models are reduced-order models used to study global circulation dynamics and transport. They provide estimates of biomarkers (such as pressure, flow rates, and concentrations) for surgery planning and…
We introduce estimatable variation neural networks (EVNNs), a class of neural networks that allow a computationally cheap estimate on the $BV$ norm motivated by the space $BMV$ of functions with bounded M-variation. We prove a universal…
Recently, a nonconforming surface finite element was developed to discretize 3d vector-valued compressible flow problems arising in climate modeling. In this contribution we derive an error analysis for this approach on a vector-valued…
Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization…
Kirigami are part of the larger class of mechanical metamaterials, which exhibit exotic properties. This article focuses on rhombi-slits, which is a specific type of kirigami. A nonlinear kinematic model was previously proposed as a second…
We propose a fast collocation method based on Krylov subspace iterative solver on general nonuniform grids for the fractional Laplacian problem, in which the fractional operator is presented in a singular integral formulation. The method is…
Image restoration requires a careful balance between noise suppression and structure preservation. While first-order total variation (TV) regularization effectively preserves edges, it often introduces staircase artifacts, whereas…
This chapter describes how a posteriori error estimates targeting a user-defined quantity of interest, using the Dual Weighted Residual (DWR) technique, can be easily applied for biomechanical simulations in current engineering practice.…
Integrating uncertainties in the design process of reinforced concrete rail bridges, in a fully probabilistic framework, makes their design more complex and challenging. To propagate these uncertainties and convey their influence on the…
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…