A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems

05/15/2021
by   Xiao Xu, et al.
0

We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem where the subdomains share "nonlocal" interfaces of the size of the nonlocal horizon. This system of nonlocal equations is first rewritten in terms of minimization of a nonlocal energy, then discretized with a meshfree approximation and finally solved via a Lagrange multiplier approach in a way that resembles the finite element tearing and interconnect method. Specifically, we propose a distributed projected gradient algorithm for the solution of the Lagrange multiplier system, whose unknowns determine the nonlocal interface conditions between subdomains. Several two-dimensional numerical tests illustrate the strong and weak scalability of our algorithm, which outperforms the standard approach to the distributed numerical solution of the problem. This work is the first rigorous numerical study in a two-dimensional multi-domain setting for nonlocal operators with finite horizon and, as such, it is a fundamental step towards increasing the use of nonlocal models in large scale simulations.

READ FULL TEXT

Authors

page 6

07/07/2021

Stability and convergence analysis of a domain decomposition FE/FD method for the Maxwell's equations in time domain

Stability and convergence analysis for the domain decomposition finite e...
06/19/2020

Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems

This work introduces a novel, fully robust and highly-scalable, h-adapti...
08/26/2020

A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions

A rigorous mathematical framework is provided for a substructuring-based...
02/08/2022

Scalable computational kernels for mortar finite element methods

Targeting simulations on parallel hardware architectures, this paper pre...
06/20/2022

A reduced order model for domain decompositions with non-conforming interfaces

In this paper we propose a reduced order modeling strategy for two-way D...
05/27/2021

Multidirectionnal sweeping preconditioners with non-overlapping checkerboard domain decomposition for Helmholtz problems

This paper explores a family of generalized sweeping preconditionners fo...
10/05/2018

A Relaxation-based Network Decomposition Algorithm for Parallel Transient Stability Simulation with Improved Convergence

Transient stability simulation of a large-scale and interconnected elect...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.