数值分析
This paper introduces a new application of the perfectly matched layer (PML) for mitigating model top wave reflections in geophysical fluid models. Typically, a strong Laplacian or Rayleigh damping sponge layer is used near the upper…
We present a fast, high-order algorithm for the free-space fractional Fokker-Planck equation (FFPE) in arbitrary spatial dimension. Its fundamental solution, corresponding to a Dirac-delta initial condition, is obtained from the explicit…
The Gauss-Seidel projection method (GSPM) constitutes an efficient and numerically stable numerical framework for micromagnetic simulations of ferromagnetic media. This scheme attains first-order temporal accuracy and second-order spatial…
Mixed-precision variants of the Jacobi algorithm for symmetric positive definite eigenproblems and the one-sided Jacobi algorithm for singular value decompositions have recently been shown to compute eigenvalues and singular values to high…
This work introduces a novel high-order numerical framework for solving kinetic equations, designed to remain uniformly valid across all regimes of the mean free path, spanning from the rarefied kinetic scale to the incompressible…
Third medium contact provides a smooth continuum alternative to classical contact algorithms by replacing explicit contact constraints with a highly compliant fictitious medium. In this work, an auxiliary-field stabilization is introduced…
The numerical reconstruction of controls for partial differential equations remains comparatively underdeveloped, despite the extensive analytical literature on controllability. This difficulty is particularly pronounced for wave equations,…
Kinetic equations are used to model a wide range of phenomena important for real-world applications. Their applications span astrophysics, nuclear physics, engineering, and social sciences. Due to their high-dimensional phase space,…
We study hp approximation and additive Schwarz decompositions for variable-order cubical finite element spaces on one-irregular meshes. For fitted homogeneous diffusion interface problems on one-irregular hexahedral meshes, we prove an…
We analyze an often used closure model for multi-material hydrodynamics where pressure temperature equilibrium (PTE) is assumed for every state; emphasis is placed on tabular equations of state. This multi-material model is often referred…
Body-fitted finite-element methods deliver high-order accuracy but hinge on a clean, watertight, conforming mesh, a requirement that breaks down for the geometrically imperfect CAD assemblies, image-based volumetric data, and voxel-native…
We study the stability of a classical family of metrics defined over functions' Gaussian scale-space representations, focusing on the comparison of images (functions of two variables). These metrics have precedents both in harmonic…
We prove two Korovkin-type approximation theorems for sequences of positive linear operators acting on continuous functions on $[0,\infty)$. Under the assumption of pointwise convergence on suitable test functions, we establish pointwise…
As the study of temporal and spatial discretization schemes continues to advance, recent work has focused on the use of Galerkin-in-time discretization schemes that enable broader structure-preservation than is known for Runge-Kutta…
A sticky diffusion is a process that can stick to and detach from a lower-dimensional boundary. A challenge in simulating such a process is in capturing the change in dimension in a dynamically consistent way. We introduce a numerical…
We propose and analyze an adaptive iterative numerical homogenization method to approximate the solution of a class of quasilinear nonmonotone elliptic problems that is of multiscale nature. The method is based on the technique of the…
We construct explicit approximations to the solution of a second-order parabolic partial differential equation on the real line with variable coefficients. The method is based on Chernoff's product formula and uses a new operator-valued…
Muon-type optimizers construct update directions for dense neural-network weights by applying a finite Newton-Schulz map to momentum-gradient matrices. For an $H \times W$ matrix, with $r=\min\{H,W\}$ and $s=\max\{H,W\}$, $K$ steps of the…
In the present paper, we introduce a numerical method for second-kind Fredholm integral equations (FIEs) based on de la Vall\'ee Poussin-type (VP) polynomial approximations at Jacobi zeros. This class of approximations offers several…
In this paper, we consider Fourier phase retrieval from differential intensity measurements, i.e., the problem of determining the phase of a complex-valued function from a series of intensity measurements differing only by slight…