Advanced Differential Quadrature Methods (Chapman & Hall/CRC by Zhi Zong

By Zhi Zong

The ebook used to be very attention-grabbing for me as my PhD thesis are hooked up with differential quadrature (DQ). It comprises relatively new informations approximately improveing of the DQM. It base on authors articles from numerous final years. The unfavourable is that the articles are shorten, so occasionally you want to search for them within the e-book info base to discover information. occasionally it isn't so transparent clarify from the place the autors receive there formulation [there might be extra references to literature] - occasionally it's attainable to discover theorems that healthy even beter to the topic. besides i'm more than happy to have this booklet because it offers me much convenient informations approximately instructions of the DQ inspiration enhance.

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Additional info for Advanced Differential Quadrature Methods (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science)

Example text

Each δt and the physical domain of 0 ≤ x ≤ π/2, 0 ≤ y ≤ π/2 form a block. Since the length scales in every block are the same, the DQ weighting coefficients can be uniformly used at different blocks. The DQ weighting coefficients are first computed in BLK1, and then stored for the application in the following blocks. At each block, applying DQ to Eqs. , L, where N and M are the numbers of mesh points in the x and y direction, respectively, L is the number of time levels in the block, a, ¯ a, and ˆ a are the DQ weighting coefficients of the first-order derivatives with respect to x, y and ¯ are the DQ weighting coefficients of the second-order derivatives t, and b, b with respect to x and y.

The DQ equations at inner grids are similar to Eq. 78). As can be seen that the symbolic expressions are similar to the ones of DQEM or GDQR, and all boundary conditions can be conveniently applied. (f ) Build-in method (3) (Wu and Liu, 2000) The build-in method (3) is also an extension of the build-in method (1), similar to the build-in method (2) described above. The essential difference (1) (1) (2) (2) from the build-in method (2) is that w1 and wN , instead of w1 and wN , are used as independent variables in computing the weighting coefficients of the third- and fourth-order derivatives.

The reduction of CPU time is not so promising. The reason is that since L is changed from 5 to 7, the number of unknowns for this case is much larger than the previous case. So, each iteration requires much more CPU time. 5, but the efficiency is greatly improved. 6. 6, it can be observed that for all the 20 blocks, the number of iterations to satisfy convergence criteria Eqs. 5. So, NTI for this case is 20 × 70 = 1400. 26 s) of the previous case. 802 From numerical experiments, it was found that the efficiency of blockmarching technique could be further improved when δt is increased from 1 to 2.

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