Toward the construction of a fourth-order difference scheme for transient EM wave simulation: staggered grid approach

1997 ◽  
Vol 45 (11) ◽  
pp. 1573-1580 ◽  
Author(s):  
J.L. Young ◽  
D. Gaitonde ◽  
J.S. Shang
Keyword(s):  
Difference Scheme ◽  
Fourth Order ◽  
Staggered Grid ◽  
Order Difference ◽  
Wave Simulation ◽  
Grid Approach

Finite Difference Modeling of Elastic Wave Propagation

2012 ◽  
Vol 433-440 ◽  
pp. 4656-4661
Author(s):  
Qiang Zhang ◽  
Qi Zhen Du ◽  
Xu Fei Gong
Keyword(s):  
Finite Difference ◽  
Elastic Wave ◽  
Difference Scheme ◽  
Transversely Isotropic ◽  
Second Order ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Order Difference ◽  
Transversely Isotropic Media ◽  
Isotropic Media

We present a staggered-grid finite difference scheme for velocity-stress equations to simulate the elastic wave propagating in transversely isotropic media. Instead of the widely used temporally second-order difference scheme, a temporally fourth-order scheme is obtained in this paper. We approximate the third-order spatial derivatives with 2N-order difference rather than second-order or other fixed order difference as before. Thus, it could be possible to make a balanced accuracy of O (Δt4+Δx2N) with arbitrary N. Related issues such as stability criterion, numerical dispersion, source loading and boundary condition are also discussed in this paper. The numerical modeling result indicates that the scheme is reliable.

scholarly journals Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yan Chang ◽  
Huanzhen Chen
Keyword(s):  
Quantum Mechanics ◽  
Difference Scheme ◽  
Fourth Order ◽  
Convergence Rates ◽  
Order Convergence ◽  
Fractional Quantum ◽  
Order Difference ◽  
Computation Cost ◽  
Fractional Schrödinger Equations ◽  
Nonlinear Fractional Schrödinger Equations

AbstractTo improve the computing efficiency, a fourth-order difference scheme is proposed and a fast algorithm is designed to simulate the nonlinear fractional Schrödinger (FNLS) equation oriented from the fractional quantum mechanics. The numerical analysis and experiments conducted in this article show that the proposed difference scheme has the optimal second-order and fourth-order convergence rates in time and space respectively, reduces its computation cost to $\mathcal{O}(M\log M)$O(MlogM), and recognizes accurately its physical feature of FNLS such as the mass balance.

Sign in / Sign up

Export Citation Format

Share Document