Yield-modeling accuracy requirements for 300-mm processing

1998 ◽  
Author(s):  
Daren L. Dance ◽  
Christopher W. Long
Keyword(s):  
Yield Modeling ◽  
Modeling Accuracy

Parameterization of Directional Spectra and Its Influence on Ship Motion Predictions

1993 ◽  
Vol 37 (02) ◽  
pp. 138-147
Author(s):  
Ross Graham ◽  
Barbara-Ann Juszko
Keyword(s):  
Spectral Data ◽  
Field Data ◽  
Ship Motion ◽  
Flight Operations ◽  
Modeling Accuracy ◽  
Directional Wave ◽  
Made In

An approach to parameterizing directional spectra proposed by Hogben & Cobb based on a combination of the Ochi & Hubble 6-parameter spectrum and the Longuet-Higgins et al cos2p model is adopted for a study of directional parameterizations and their influence on ship motion predictions. Two schemes for evaluating the directional spreading parameters are assessed in terms of their ability to reproduce highly resolved measured directional spectra, and the best approach, termed the 10-parameter spectrum, is adopted. The applicability of the 10-parameter spectrum to hindcast spectra is investigated, and acceptable fits obtained for 93% of the spectra considered. An evaluation of the ability of the hindcast model to reproduce the measured spectral data is also made. In general, it is found that the differences between the hindcast spectra and associated 10-parameter fits are significantly smaller than the differences between the hindcast spectra and the field data, and it is concluded that the 10-parameter spectrum is a suitable basis for developing statistical descriptions of directional wave climates. The effects of directional parameterization on ship motion predictions are investigated by computing the ship responses as a function of heading for sample hindcast spectra, and the associated 10-parameter and Bretschneider 2-parameter spectra. The responses calculated using the 10-parameter spectrum are found to be in better agreement with the hindcast results than those obtained with the Bretschneider 2-parameter spectrum, with a significant improvement in modeling accuracy in the case of bi-modal spectra. The potential advantages of incorporating the 10-parameter spectrum in future operability analyses of flight operations is examined by comparing the head-to-wind roll response computed using hindcast spectra with that predicted using 10-parameter and Bretschneider spectra.

Pseudoacoustic tilted transversely isotropic modeling with optimal k-space operator-based implicit finite-difference schemes

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. T139-T157 ◽  
Author(s):  
Shigang Xu ◽  
Yang Liu
Keyword(s):  
Finite Difference ◽  
Spatial Modeling ◽  
Wave Equations ◽  
Transversely Isotropic ◽  
Dispersion Relations ◽  
High Order ◽  
Space Operator ◽  
Modeling Accuracy ◽  
Tti Media ◽  
Temporal And Spatial

Current temporal high-order finite-difference (FD) stencils are mainly designed for isotropic wave equations, which cannot be directly extended to pseudoacoustic wave equations (PWEs) in tilted transversely isotropic (TTI) media. Moreover, it is difficult to obtain the time-space domain FD coefficients for anisotropic PWEs based on nonlinear dispersion relations in which anisotropy parameters are coupled with FD coefficients. Therefore, a second-order FD for temporal derivatives and a high-order FD for spatial derivatives are commonly used to discretize PWEs in TTI media. To improve the temporal and spatial modeling accuracy further, we have developed several effective FD schemes for modeling PWEs in TTI media. Through combining the [Formula: see text] (wavenumber)-space operators with the conventional implicit FD stencils (i.e., regular-grid [RG], staggered-grid [SG], and rotated SG [RSG]), we establish novel dispersion relations and determine FD coefficients using least-squares (LS). Based on [Formula: see text]-space operator compensation, we adopt the modified LS-based implicit RG-FD, implicit SG-FD, and implicit RSG-FD methods to respectively solve the second- and first-order PWEs in TTI media. Dispersion analyses indicate that the modified implicit FD schemes based on [Formula: see text]-space operator compensation can greatly increase the numerical accuracy at large wavenumbers. Modeling examples in TTI media demonstrate that the proposed FD schemes can adopt a short FD operator to simultaneously achieve high temporal and spatial modeling accuracy, thus significantly improve the computational efficiency compared with the conventional methods.

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