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3. Accuracy verification To verify the accuracy of FMBEM, two models with 1 inclusion centered at the origin of the matrix and 343 (7x7x7) inclusions that are periodically distributed are used, as shown in Fig. 18. 1. Each inclusion is discretized into 392 triangle piecewise constant elements and 120,000 elements for the outer boundary of matrix. OxlO"7. it f * . 0) - u\ ' and the traction ry are given in Fig. 19. The slight difference of the last 49 inclusions, which are near the front surface (in +JC direction) of the matrix, comes from matrix discretization error.

1985; 60: 187-207. 2. Greengard L, Rokhlin V. A fast algorithm for particle simulations. J. Comput. , 1987; 73: 325-348. 3. Greengard L, Rokhlin V. A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica, 1997; 6: 229-269. 4. Nishimura N. Fast multipole accelerated boundary integral equation methods. Applied Mechanics Review, 2002; 55: 299-324. 5. Peirce AP, Napier JAL. A spectral multipole method for efficient solutions of large scale boundary element models in elastostatics.

21 shows the computing time versus numbers of processors and the speedup for the parallel FMBEM. ' „ ^ > 3 ? '-■".. 2 Number of DOF 477,600 948,000 1,536,000 2,712,000 3,888,000 5,064,000 Memory requirement (MB) 1,976 3,070 4,067 5,989 7,543 9,182 Computing time (s) 4,660 15,179 32,136 71,636 103,635 161,190 90000 ideal adlkJ speedUfJ --- \> X . y f g. /-'"" ,> , , ■ ■ • " - " 40000 , - - ■ ' 30000 20000 \ 10000 -.... _. _ 10 12 14 16 18 20 Number of processors 22 24 26 29 M 32 y /•"' 18 20 Number of processors 22 24 26 28 30 32 Figure 2 1 : The computing time versus number of processors (left), and the speedup for parallel F M B E M 5.

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Airbus A320 SOP 09After Landing


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