scholarly journals Obtaining artificial boundary conditions for fractional sub-diffusion equation on space two-dimensional unbounded domains

2014 ◽  
Vol 68 (1-2) ◽  
pp. 13-26 ◽  
Author(s):  
Rezvan Ghaffari ◽  
S. Mohammad Hosseini
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Unbounded Domains ◽  
Two Dimensional ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions

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.

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.

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