Exact artificial boundary conditions of 1D semi-discretized peridynamics

02/25/2020
by   Songsong Ji, et al.
0

The peridynamic theory reformulates the equations of continuum mechanics in terms of integro-differential equations instead of partial differential equations. It is not trivial to directly apply naive approach in artificial boundary conditions for continua to peridynamics modeling, because it usually involves semi-discretization scheme. In this paper, we present a new way to construct exact boundary conditions for semi-discretized peridynamics using kernel functions and recursive relations. Specially, kernel functions are used to characterize one single source are combined to construct the exact boundary conditions. The recursive relationships between the kernel functions are proposed, therefore the kernel functions can be computed through the ordinary differential system and integral system with high precision. The numerical results demonstrate that the boundary condition has high accuracy. The proposed method can be applied to modeling of wave propagation of other nonlocal theories and high dimensional cases.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 3

page 12

page 16

11/30/2020

A New Treatment of Boundary Conditions in PDE Solutions with Galerkin Methods via Partial Integral Equation Framework

We present a new framework for solution of Partial Differential Equation...
08/18/2021

High accuracy power series method for solving scalar, vector, and inhomogeneous nonlinear Schrödinger equations

We develop a high accuracy power series method for solving partial diffe...
08/18/2021

Bulk-surface Lie splitting for parabolic problems with dynamic boundary conditions

This paper studies bulk-surface splitting methods of first order for (se...
05/06/2022

On boundary conditions parametrized by analytic functions

Computer algebra can answer various questions about partial differential...
08/15/2021

Integral boundary conditions in phase field models

Modeling the microstructure evolution of a material embedded in a device...
04/13/2021

Finite Volume Neural Network: Modeling Subsurface Contaminant Transport

Data-driven modeling of spatiotemporal physical processes with general d...
03/06/2018

On Nonlinear Dimensionality Reduction, Linear Smoothing and Autoencoding

We develop theory for nonlinear dimensionality reduction (NLDR). A numbe...
This week in AI

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