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11/22/2022
Minimal positive stencils in meshfree finite difference methods for linear elliptic equations in non-divergence form
We design a monotone meshfree finite difference method for linear ellipt...
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03/01/2022
Nonlocal diffusion models with consistent local and fractional limits
For some spatially nonlocal diffusion models with a finite range of nonl...
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02/14/2022
A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials
In this work we aim to develop a unified mathematical framework and a re...
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01/28/2022
Efficient optimization-based quadrature for variational discretization of nonlocal problems
Casting nonlocal problems in variational form and discretizing them with...
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07/15/2021
A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems
We present a Petrov-Gelerkin (PG) method for a class of nonlocal convect...
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07/03/2021
An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems
In this paper we present an asymptotically compatible meshfree method fo...
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02/04/2020
Numerical methods for nonlocal and fractional models
Partial differential equations (PDEs) are used, with huge success, to mo...
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01/02/2020
Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation
In this work, we study the reproducing kernel (RK) collocation method fo...
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09/02/2019
Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues
In this work, we review the connection between the subjects of homogeniz...
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07/28/2019
Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion
Reproducing kernel (RK) approximations are meshfree methods that constru...
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05/20/2019