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81.
82.
Many problems based on unstructured grids provide a natural multigrid framework due to using an adaptive gridding procedure.
When the grids are saved, even starting from just a fine grid problem poses no serious theoretical difficulties in applying
multigrid. A more difficult case occurs when a highly unstructured grid problem is to be solved with no hints how the grid
was produced. Here, there may be no natural multigrid structure and applying such a solver may be quite difficult to do.
Since unstructured grids play a vital role in scientific computing, many modifications have been proposed in order to apply
a fast, robust multigrid solver. One suggested solution is to map the unstructured grid onto a structured grid and then apply
multigrid to a sequence of structured grids as a preconditioner.
In this paper, we derive both general upper and lower bounds on the condition number of this procedure in terms of computable
grid parameters. We provide examples to illuminate when this preconditioner is a useful (e. g.,p orh-p formulated finite element problems on semi-structured grids) or should be avoided (e.g., typical computational fluid dynamics
(CFD) or boundary layer problems). We show that unless great care is taken, this mapping can lead to a system with a high
condition number which eliminates the advantage of the multigrid method.
This work was partially supported by ONR Grant # N0014-91-J-1576. 相似文献
83.
G.K MorL.K Malhotra 《Solid State Communications》2003,125(10):523-528
Restricting the palladium cap layer thickness to ≤9 nm on top of 170 nm Pr films during in situ hydrogen loading has been shown to result in nanocrystallite size PrH3−δ films even though the deposited Pr films are of large crystallite size. The effect is attributed to hydrogen-induced stresses in the PrH3−δ films, which trigger structural rearrangement. These nanocrystalline films show a blue shift of the transmittance edge with respect to PrH3−δ films of large crystallite size. The approximate size of the nanocrystallites calculated from the blue shift using an effective mass approximation (EMA) theory is supported by XRD, TEM and AFM measurements. 相似文献
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86.
J. Leonard S. L. Malhotra 《Journal of polymer science. Part A, Polymer chemistry》1974,12(10):2391-2401
220 MHz NMR spectra of sample of poly-p-isopropyl-α-methylstyrene prepared through anionic (A) and cationic (B) polymerizations are studied. Peaks at τ values of 9.07, 9.41, and 9.71 are assigned to isotactic (i), heterotactic (h), and syndiotactic (s) α-methyl triads, respectively. From the α-methyl triads and the β-proton tetrads it is found that polymer A deviates little from Bernoullian statistics and that first-order Markov configurational statistics applies to polymer B. Isopropyl methine and methyl proton resonances are also analyzed in terms of the configurational statistics of the polymer. Resonances of the phenyl protons are assigned with increasing field to s, h, i meta and ortho protons. 相似文献
87.
Kumaran Ramanathan M.N. Kamalasanan B.D. Malhotra D.R. Pradhan S. Chandra 《Journal of Sol-Gel Science and Technology》1997,10(3):309-316
Physical adsorption and physical entrapment techniques have been utilized for the immobilization of lactate dehydrogenase (LDH) on tetraethylorthosilicate (TEOS) derived sol-gel films. The enzyme (LDH) activity has been assayed as a function of time, temperature, pH and pyruvate concentration. The results of photometric measurements used for monitoring the reaction yield a response time of about 1 min, linearity over a concentration range of 0–1.5 × 10-3 M and detection limit of 5 × 10-5 M. The TEOS sol-gel films containing LDH have been found to be stable for about 30 days at temperatures 4 to 10°C. 相似文献
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A d.c. arc emission spectrographic method has been developed for the determination of nine trace impurities in boron nitride. The charge for exciting the sample contains equal quantities of boron nitride and graphite (containing 2% NaF as carrier and 1% La(2)O(3) as an internal standard). The method is useful in the determination of impurities in the range 2-1000 ppm, with a mean relative standard deviation of 13%. 相似文献