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оригинального документа
: http://num-meth.srcc.msu.ru/english/zhurnal/tom_2014/v15r144.html
Дата изменения: Mon Sep 8 14:19:33 2014 Дата индексирования: Sun Apr 10 03:05:42 2016 Кодировка: IBM-866 |
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"A 3D Helmholtz iterative solver with a semi-analytical preconditioner
for acoustic wavefield modeling in seismic exploration problems" Neklyudov D.A., Silvestrov I.Yu., and Tcheverda V.A. |
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An approach to the iterative solution of the 3D acoustic wave equation in a frequency domain is proposed, substantiated, and verified numerically. Our method is based on Krylov-type linear solvers, similarly to several other iterative solver approaches. The distinctive feature of our method is the use of a right preconditioner obtained as the solution of the complex dumped Helmholtz equation in a 1D medium, where velocities vary only with depth. The actual Helmholtz operator is represented as a perturbation of the preconditioner. As a result, a matrix-by-vector multiplication of the preconditioned system can be efficiently evaluated via 2D FFT in x and y directions followed by the solution of a number of ordinary differential equations in z directions. While solving ODE's. it is possible to treat the 1D velocity function as a piecewise constant one and to search for the exact solution as a superposition of upgoing and downgoing waves. This approach allows one not to use explicit finite-difference approximations of derivatives at all. The method has excellent dispersion properties in both lateral and vertical directions. Keywords: Helmholtz equation, iterative methods, preconditioners, acoustic waves, seismic exploration.
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