数值分析
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…
Dual-space multilevel kernel-splitting (DMK) is a fast summation framework that combines ideas from the fast multipole method, Ewald summation, and multilevel summation. Originally formulated for free-space problems, and later extended to…
In this paper we study the dynamics of relativistic detonation waves theoretically and numerically. The reaction is physically accounted for by an extra term in the definition of the total energy density and by an additional equation for…
In this paper we develop fast numerical algorithms for solving shifted linear systems with semidefinite quasiseparable matrices. A combination of Givens and hyperbolic plane rotations is used to update the Cholesky-type factorization of the…
High-dimensional tensor data streams arise naturally in scientific and engineering applications, such as simulations of kinetic equations and quantum systems, where samples become available sequentially and are often already represented in…
We introduce an accelerated Langevin-based sampling method that is based on two complementary devices: \emph{SamAdams} adaptive timestepping, which automatically shrinks the effective integration step in stiff regions of phase space using a…
We introduce a particle method for the numerical approximation of time-dependent first-order Mean Field Games (MFGs) systems with non-separable, displacement monotone Hamiltonians and terminal costs, for arbitrary time-horizons and…