Optimized explicit finite-difference schemes for spatial derivatives using maximum norm
作者单位：Institute of Geology and GeophysicsChinese Academy of Sciences
会议名称：《中国科学院地质与地球物理研究所2013年度（第13届）学术年会》
会议日期：2014年
学科分类：081801[工学-矿产普查与勘探] 081802[工学-地球探测与信息技术] 08[工学] 0818[工学-地质资源与地质工程]
基 金：supported by the National Natural Science Foundation of China(Grant No.41074092 and 41130418) the National Major Project of China(Grant No.2011ZX05008-006)
关 键 词：Optimized scheme Explicit finite-difference Numerical dispersion Maximum norm Simulated annealing algorithm
摘 要：Conventional explicit finite-difference methods have difficulties in handling high-frequency components due to strong numerical *** can reduce the numerical dispersions by optimizing the constant coefficients of the finite-difference *** from traditional optimized schemes that use the 2-norm and the least squares,we propose to construct the objective functions using the maximum norm and solve the objective functions using the simulated annealing *** theoretical analyses and numerical experiments show that our optimized scheme is superior to traditional optimized schemes with regard to the following three ***,it provides us with much more flexibility when designing the objective functions;thus we can use various possible forms and contents to make the objective functions more ***,it allows for tighter error limitation,which is shown to be necessary to avoid rapid error accumulations for simulations on large-scale models with long travel ***,it is powerful to obtain the optimized coefficients that are much closer to the theoretical limits,which means greater savings in computational efforts and memory demand.