相关论文: Divergence-free Interpolation of Vector Fields Fro…
Magnetic fields are known to be dynamically important in the interstellar medium of our own Galaxy, and they are ubiquitously observed in diffuse gas in the halos of galaxies and galaxy clusters. Yet, magnetic fields have typically been…
We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type. These bounds require the discretization…
Highly accurate simulations of problems including second derivatives on complex geometries are of primary interest in academia and industry. Consider for example the Navier-Stokes equations or wave propagation problems of acoustic or…
In this paper, we propose an efficient quadratic interpolation formula utilizing solution gradients computed and stored at nodes and demonstrate its application to a third-order cell-centered finite-volume discretization on tetrahedral…
An integrated system of hardware and software allowing precise definition of arbitrarily oriented magnetic fields up to |B| = 1 {\mu}T within a five-layer mumetal shield is described. The system is calibrated with reference to magnetic…
A celebrated method for Variational Inequalities (VIs) is Extragradient (EG), which can be viewed as a standard discrete-time integration scheme. With this view in mind, in this paper we show that EG may suffer from discretization bias when…
We propose a novel discretization of tangent vector fields for triangle meshes. Starting with a Phong map continuously assigning normals to all points on the mesh, we define an extrinsic bases for continuous tangent vector fields by using…
We consider viscous free-boundary magnetohydrodynamics(MHD) under vacuum in $\mathbb{R}^3$, especially when vacuum magnetic field is identically zero. It is a central problem in mathematics to perform vanishing viscosity limit to get a…
Diffraction-based methods have become an invaluable tool for the detailed assessment of residual strain and stress within experimental mechanics. These methods typically measure a component of the average strain within a gauge volume. It is…
We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid…
A simple and stable method for computing accurate expectation values of observable with Variational Monte Carlo (VMC) or Diffusion Monte Carlo (DMC) algorithms is presented. The basic idea consists in replacing the usual ``bare'' estimator…
We present a computational method for reconstructing a vector field on a convex polytope $\mathcal{P} \subset \mathbb{R}^d$ of arbitrary dimension from discrete samples. We specifically address the scenario where the vector field is subject…
We propose and analyze two convection quasi-robust and pressure robust finite element methods for a fully nonlinear time-dependent magnetohydrodynamics problem. Both methods employ the $H_{\rm div}$ conforming BDM element coupled with an…
In this paper, we show that diagonal-norm summation by parts (SBP) discretizations of general non-conservative systems of hyperbolic balance laws can be rewritten as a finite-volume-type formula, also known as flux-differencing formula, if…
We study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also…
The aim of this paper is to present an extragradient method for variational inequality associated to a point-to-set vector field in Hadamard manifolds and to study its convergence properties. In order to present our method the concept of…
Null points are important locations in vector fields, such as a magnetic field. A new technique (a trilinear method for finding null points) is presented for finding null points over a large grid of points, such as those derived from a…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation…
Dynamic Programming (DP) suffers from the well-known ``curse of dimensionality'', further exacerbated by the need to compute expectations over process noise in stochastic models. This paper presents a Monte Carlo-based sampling approach for…