TY - JOUR
T1 - Efficient Simulation of Wave Propagation with Implicit Finite Difference Schemes
AU - Wensheng Zhang, Li Tong & Eric T. Chung
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 205
EP - 228
PY - 2012
DA - 2012/05
SN - 5
DO - http://doi.org/10.4208/nmtma.2011.m1026
UR - https://global-sci.org/intro/article_detail/nmtma/5935.html
KW - Acoustic wave equation, implicit schemes, ADI, LOD, stability condition, dispersion
curve, MPI parallel computations.
AB - <p style="text-align: justify;">Finite difference method is an important methodology in the approximation of waves.
In this paper, we will study two implicit finite difference schemes
for the simulation of waves. They are the weighted
alternating direction implicit (ADI) scheme and the
locally one-dimensional (LOD) scheme. The approximation errors,
stability conditions, and dispersion relations for both schemes
are investigated. Our analysis shows that the LOD implicit scheme
has less dispersion error than that of the ADI scheme. Moreover, the
unconditional stability for both schemes with arbitrary spatial accuracy
is established for the first time. In order to improve
computational efficiency, numerical algorithms based on message
passing interface (MPI) are implemented. Numerical examples of wave propagation
in a three-layer model and a standard complex model are presented.
Our analysis and comparisons show that both ADI and LOD schemes
are able to efficiently and accurately simulate wave propagation
in complex media.</p>