13 citations · 13 across the 3 of their papers we have counts for
5 papers
Sensitivity analysis for solutions to heterogeneous nonlocal systems
Nicole Buczkowski, Mikil Foss, Michael Parks +1
The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators app…
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications
Guofei Pang, Marta D'Elia, Michael Parks +1
Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integral equations with sparse, noisy, unstructured, and multi-fidelity…
An asymptotically compatible meshfree quadrature rule for non-local problems with applications to peridynamics
Nathaniel Trask, Huaiqian You, Yue Yu +1
We present a meshfree quadrature rule for compactly supported non-local integro-differential equations (IDEs) with radial kernels. We apply this rule to develop a strong-form meshf…
A block Recycled GMRES method with investigations into aspects of solver performance
Michael L. Parks, Kirk M. Soodhalter, Daniel B. Szyld
We propose a block Krylov subspace version of the GCRO-DR method proposed in [Parks et al.; SISC 2005], which is an iterative method allowing for the efficient minimization of the…
Variational Theory and Domain Decomposition for Nonlocal Problems
Burak Aksoylu, Michael L. Parks
In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish…