Zobrazeno 1 - 10
of 149
pro vyhledávání: '"TIAN Xiaochuan"'
In this paper, we consider a class of discontinuous Galerkin (DG) methods for one-dimensional nonlocal diffusion (ND) problems. The nonlocal models, which are integral equations, are widely used in describing many physical phenomena with long-range i
Externí odkaz:
http://arxiv.org/abs/2408.07261
The classical Fokker-Planck equation (FPE) is a key tool in physics for describing systems influenced by drag forces and Gaussian noise, with applications spanning multiple fields. We consider the fractional Fokker-Planck equation (FFPE), which model
Externí odkaz:
http://arxiv.org/abs/2407.15315
We prove two compactness results for function spaces with finite Dirichlet energy of half-space nonlocal gradients. In each of these results, we provide sufficient conditions on a sequence of kernel functions that guarantee the asymptotic compact emb
Externí odkaz:
http://arxiv.org/abs/2404.09079
We present a study on asymptotically compatible Galerkin discretizations for a class of parametrized nonlinear variational problems. The abstract analytical framework is based on variational convergence, or Gamma-convergence. We demonstrate the broad
Externí odkaz:
http://arxiv.org/abs/2402.07749
The paper introduces a new meshfree pseudospectral method based on Gaussian radial basis functions (RBFs) collocation to solve fractional Poisson equations. Hypergeometric functions are used to represent the fractional Laplacian of Gaussian RBFs, ena
Externí odkaz:
http://arxiv.org/abs/2312.17461
We develop a machine learning approach to identifying parameters with steady-state solutions, locating such solutions, and determining their linear stability for systems of ordinary differential equations and dynamical systems with parameters. Our ap
Externí odkaz:
http://arxiv.org/abs/2312.10315
Autor:
Han, Zhaolong, Tian, Xiaochuan
This work contributes to nonlocal vector calculus as an indispensable mathematical tool for the study of nonlocal models that arises in a variety of applications. We define the nonlocal half-ball gradient, divergence and curl operators with general k
Externí odkaz:
http://arxiv.org/abs/2212.13720
Autor:
Ye, Qihao, Tian, Xiaochuan
We design a monotone meshfree finite difference method for linear elliptic equations in the non-divergence form on point clouds via a nonlocal relaxation method. The key idea is a novel combination of a nonlocal integral relaxation of the PDE problem
Externí odkaz:
http://arxiv.org/abs/2211.12490
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter $\delta$, we review their formulation defined on a bounded domain subject to various conditions that correspond to some inhomog
Externí odkaz:
http://arxiv.org/abs/2203.00167
Autor:
Fan, Yiming, You, Huaiqian, Tian, Xiaochuan, Yang, Xiu, Li, Xingjie, Prakash, Naveen, Yu, Yue
In this work we aim to develop a unified mathematical framework and a reliable computational approach to model the brittle fracture in heterogeneous materials with variability in material microstructures, and to provide statistic metrics for quantiti
Externí odkaz:
http://arxiv.org/abs/2202.06578