A Finite-Difference Scheme Based on PML Boundary Condition with High Power Grid Step Variation

2011 ◽  
Vol 54 (3) ◽  
pp. 393-402 ◽  
Author(s):  
Lin-Jie SUN ◽  
Xing-Yao YIN
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Difference Scheme ◽  
High Power ◽  
Finite Difference Scheme ◽  
Power Grid ◽  
Grid Step

scholarly journals A finite difference scheme for a fluid dynamic traffic flow model appended with two-point boundary condition

2012 ◽  
Vol 31 ◽  
pp. 43-52 ◽  
Author(s):  
MO Gani ◽  
MM Hossain ◽  
LS Andallah
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Difference Scheme ◽  
Traffic Flow ◽  
Finite Difference Scheme ◽  
Flow Model ◽  
Fluid Dynamic ◽  
Point Boundary ◽  
Traffic Flow Model ◽  
First Order

A fluid dynamic traffic flow model with a linear velocity-density closure relation is considered. The model reads as a quasi-linear first order hyperbolic partial differential equation (PDE) and in order to incorporate initial and boundary data the PDE is treated as an initial boundary value problem (IBVP). The derivation of a first order explicit finite difference scheme of the IBVP for two-point boundary condition is presented which is analogous to the well known Lax-Friedrichs scheme. The Lax-Friedrichs scheme for our model is not straight-forward to implement and one needs to employ a simultaneous physical constraint and stability condition. Therefore, a mathematical analysis is presented in order to establish the physical constraint and stability condition of the scheme. The finite difference scheme is implemented and the graphical presentation of numerical features of error estimation and rate of convergence is produced. Numerical simulation results verify some well understood qualitative behavior of traffic flow.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10307GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 43-52

scholarly journals Cosine-type weighted hybrid absorbing boundary based on the second-order Higdon boundary condition and its GPU implementation

2020 ◽  
Vol 17 (2) ◽  
pp. 231-248
Author(s):  
Chuang Xie ◽  
Peng Song ◽  
Jun Tan ◽  
Baohua Liu ◽  
Jinshan Li ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Second Order ◽  
Gpu Acceleration ◽  
Processing Unit ◽  
Hybrid Mode ◽  
Absorption Effect ◽  
Absorbing Boundary

Abstract In this paper, we analyze the absorption effect of the hybrid absorbing boundary condition (ABC) with various hybrid modes, and propose a cosine-type optimized weighted hybrid mode taking into account the boundary reflection intensity of the inner and outer boundaries of transition area. Additionally, we derive a new finite-difference scheme of the second-order Higdon ABC and the corner equation for Graphic Processing Unit (GPU) acceleration. On this basis, a new type of second-order Higdon hybrid ABC applicable for GPU acceleration is established in the acoustic finite-difference modeling. Numerical experiments demonstrate that the proposed cosine-type weighted hybrid mode can achieve a better absorption effect compared with other weighted hybrid modes; the second-order Higdon ABC based on the proposed new finite-difference scheme can effectively improve the GPU speed-up ratio and is more effective in large-scale wavefield high-precision simulation based on GPU acceleration.

Sign in / Sign up

Export Citation Format

Share Document