A Means for the Construction of Difference Schemes with Higher Order of Approximation

Author(s):  
Yu. I. Shokin
1966 ◽  
Vol 19 (2) ◽  
pp. 627-634 ◽  
Author(s):  
Mari J. K. Brown

Free recall of lists at different orders of approximation to English was compared to the recall of the same lists when the order of the words had been scrambled to destroy their sequential organization. Recall of the organized lists showed the typical improvement with increasing order of approximation. Recall of the scrambled lists was unrelated to the original order of approximation. The results indicate that increased recall with increasing order of approximation to English is not produced by systematic differences in the characteristics of the individual words comprising the approximations. When recall of the organized lists was scored in terms of the number of longer sequences present in recall, the number of recalled sequences of any given length increased as order of approximation to English increased, with the first order list showing proportionally less organization in recall than the second and higher order lists.


Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. T69-T82 ◽  
Author(s):  
Shen Wang ◽  
Jianlin Xia ◽  
Maarten V. de Hoop ◽  
Xiaoye S. Li

We considered the discretization and approximate solutions of equations describing time-harmonic qP-polarized waves in 3D inhomogeneous anisotropic media. The anisotropy comprises general (tilted) transversely isotropic symmetries. We are concerned with solving these equations for a large number of different sources. We considered higher-order partial differential equations and variable-order finite-difference schemes to accommodate anisotropy on the one hand and allow higher-order accuracy — to control sampling rates for relatively high frequencies — on the other hand. We made use of a nested dissection based domain decomposition in a massively parallel multifrontal solver combined with hierarchically semiseparable matrix compression techniques. The higher-order partial differential operators and the variable-order finite-difference schemes require the introduction of separators with variable thickness in the nested dissection; the development of these and their integration with the multifrontal solver is the main focus of our study. The algorithm that we developed is a powerful tool for anisotropic full-waveform inversion.


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