scholarly journals Artificial boundary conditions for parabolic Volterra integro-differential equations on unbounded two-dimensional domains

2006 ◽  
Vol 197 (2) ◽  
pp. 406-420 ◽  
Author(s):  
Houde Han ◽  
Liang Zhu ◽  
Hermann Brunner ◽  
Jingtang Ma
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions

A Comparative Study of Artificial Boundary Conditions in ABAQUS

2013 ◽  
Vol 671-674 ◽  
pp. 1386-1389
Author(s):  
Yan Wei Wang ◽  
Shan You Li ◽  
Qiang Ma ◽  
Wei Li
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Element Model ◽  
The Other ◽  
Two Dimensional ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions ◽  
Dimensional Finite Element ◽  
Viscous Boundary ◽  
Better Than

Viscous boundary, viscous spring boundary, infinite boundary have been widely used during the last decades to solve the wave propagation in the infinite ground. In this paper we evaluate the performance of the three boundary conditions focusing on their solution precision. The comparison is performed on a two dimensional finite element model built by ABAQUS. The results show that viscous spring boundary outperforms the other boundary conditions, and viscous boundary is better than infinite element.

Split Local Artificial Boundary Conditions for the Two-Dimensional Sine-Gordon Equation on R2

2011 ◽  
Vol 10 (5) ◽  
pp. 1161-1183 ◽  
Author(s):  
Houde Han ◽  
Zhiwen Zhang
Keyword(s):  
Boundary Conditions ◽  
Gordon Equation ◽  
Splitting Method ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Computational Domain ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions

AbstractIn this paper the numerical solution of the two-dimensional sine-Gordon equation is studied. Split local artificial boundary conditions are obtained by the operator splitting method. Then the original problem is reduced to an initial boundary value problem on a bounded computational domain, which can be solved by the finite difference method. Several numerical examples are provided to demonstrate the effectiveness and accuracy of the proposed method, and some interesting propagation and collision behaviors of the solitary wave solutions are observed.

Numerical Solution of the Time-Fractional Sub-Diffusion Equation on an Unbounded Domain in Two-Dimensional Space

2017 ◽  
Vol 7 (3) ◽  
pp. 439-454 ◽  
Author(s):  
Hongwei Li ◽  
Xiaonan Wu ◽  
Jiwei Zhang
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Unbounded Domain ◽  
Dimensional Space ◽  
Fourier Series Expansion ◽  
Computational Domain ◽  
Two Dimensional ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions

AbstractThe numerical solution of the time-fractional sub-diffusion equation on an unbounded domain in two-dimensional space is considered, where a circular artificial boundary is introduced to divide the unbounded domain into a bounded computational domain and an unbounded exterior domain. The local artificial boundary conditions for the fractional sub-diffusion equation are designed on the circular artificial boundary by a joint Laplace transform and Fourier series expansion, and some auxiliary variables are introduced to circumvent high-order derivatives in the artificial boundary conditions. The original problem defined on the unbounded domain is thus reduced to an initial boundary value problem on a bounded computational domain. A finite difference and L1 approximation are applied for the space variables and the Caputo time-fractional derivative, respectively. Two numerical examples demonstrate the performance of the proposed method.

scholarly journals Accurate artificial boundary conditions for semi-discretized one-dimensional peridynamics

2021 ◽  
Vol 477 (2250) ◽  
pp. 20210229
Author(s):  
Songsong Ji ◽  
Gang Pang ◽  
Jiwei Zhang ◽  
Yibo Yang ◽  
Paris Perdikaris
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
High Dimensional ◽  
Green Functions ◽  
Artificial Boundary ◽  
Wave Source ◽  
Single Wave ◽  
One Dimensional ◽  
Artificial Boundary Conditions ◽  
Non Local

The peridynamic theory reformulates the equations of continuum mechanics in terms of integro-differential equations instead of partial differential equations. In this paper, we consider the construction of artificial boundary conditions (ABCs) for semi-discretized peridynamics using Green functions. Especially, the Green functions that represent the response to the single wave source are used to construct the accu2rate boundary conditions. The recursive relationships between the Green functions are proposed, therefore the Green functions can be computed through a differential and integral system with high precision. The numerical results demonstrate the accuracy of the proposed ABCs. The proposed method can be applied to modelling of wave propagation for other non-local theories and high-dimensional cases.

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