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Tensor computations are gaining wide adoption in big data analysis and artificial intelligence. Among them, tensor completion is used to predict the missing or unobserved value in tensors. The decomposition-based tensor completion algorithms have attracted significant research attention since they exhibit better parallelization and scalability. However, existing optimization techniques for tensor completion cannot sustain the increasing demand for applying tensor completion on ever larger tensor data. To address the above limitations, we develop the first tensor completion library cuTC on multiple Graphics Processing Units (GPUs) with three widely used optimization algorithms such as alternating least squares (ALS), stochastic gradient descent (SGD) and coordinate descent (CCD+). We propose a novel TB-COO format that leverages warp shuffle and shared memory on GPU to enable efficient reduction. In addition, we adopt the auto-tuning method to determine the optimal parameters for better convergence and performance. We compare cuTC with state-of-the-art tensor completion libraries on real-world datasets, and the results show cuTC achieves significant speedup with similar or even better accuracy. CCS CONCEPTS• Computer systems organization → Parallel architectures; • Computing methodologies → Parallel algorithms.

Summary. The pressure attenuation of a submerged, nonfree jet has been studied with a simulated wellbore. Equations describing pressure attenuation along the centerline and the cross-sectional pressure distribution of the jet are given. With these equations, bottomhole hydraulic parameters can then be calculated. Also, an optimal design of a jet-drilling hydraulic program based on bottomhole parameters has been developed. Introduction The application of jet drilling has put well drilling on a technically well-founded basis. It becomes clear that penetration rate and drilling cost depend to a large extent on the bottomhole hydraulic parameters, which are closely related to jet action. Because the con-dition of well drilling is complicated, however, and no reliable an practical calculation of drilling jet is available, hydraulic design cannot be made in terms of effective bottomhole jet performance. Therefore, improvement of drilling efficiency is still a problem to be solved. For jet bits commonly used, the distance between the nozzle and the bottom is more than 100 mm [3.9 in.]. In addition to the energy loss in the drillstring and annulus, the power loss of the jet across this distance is also significant. Therefore, to optimize the hydraulic parameters, both losses should be taken into consideration. A laboratory study on a submerged, nonfree jet has been made systematically to clarify the attenuation of jet power and pressure. Thereby, a new method for the calculation of bottomhole hydraulic parameters and an optimal design of a jet-drilling hydraulic program have been proposed. Its application can be extended to cleaning, cutting, and breaking action by hydraulic means. Experimental Equipment The drilling-jet simulation equipment is composed mainly of a circulating system and a measuring system. The circulating system comprises a water tank, plunger pumps, a pressure filter, a 24.4-cm [9 5/8.-in.] simulated wellbore, a measuring tank, and a centrifugal pump. There are viewing windows on the wall of the wellbore, and a jet nozzle seat and an overflow port on the top. The measuring system includes Pitot tubes and multipoint pressure-measuring plates, pressure transducers, digital volunteers, and a printer. The Pitot tube is used to measure the pressure of the jet at any point. The multipoint pressure-measuring plate is used to measure the pressures of the jet at several points with crossflow, which is formed from impingement of the jet on the measuring plate to evaluate the influence of crossflow. Centerline Jet Pressure Attenuation and Cross-Sectional Pressure Distribution Different nozzle channels (cone and streamline), nozzle sizes (2.80, 3.74, 4.85, 7, 8, and 9 mm [0.11, 0.15, 0.19, 0.28, 0.31, and 0.35 in.]), and jet velocities (40 to 140 m/s [131 to 459 ft/sec]) were used in the experiment. The Reynolds number ranged from 1.18 × 10–5 to 10.25 × 10–5. Clean water was used, but sometimes aqueous solutions of carboxymethylcellulose (CMC) and polyacrylamide (PAM) were used to duplicate the experiment. Influence of Jet Velocity on Pressure Attenuation. Experiments have shown that as the jet velocity increases, the centerline jet pressure attenuation decreases. Fig. 1 shows the experimental result without crossflow. The jet was generated by a cone-shaped nozzle (dn,= 2.80 mm [0.11 in.]) and measured by the Pitot tube. Figs. 2 and 3 show the experimental results with crossflow. The jets were generated by a cone-shaped nozzle (d, = 3.74 mm [0.15 in.]) and a streamline nozzle (dn =9 mm [0.35 in.]), respectively, and were measured by the multipoint pressure-measuring plate in both cases. The figures show that the effects of jet velocity are similar for different nozzles, because the jet velocity increases as the dimensionless attenuation curve moves upward. For example, with L/dn, = 10 in Fig. 1, pc/pn =0.36 for a jet velocity of 42.31 m/s [138.8 ft/sec]. With the same ratio of L/dn, pc,/pn =0.74 for a jet velocity of 107.30 m/s [352 ft/sec] and pc/pn, rises to 0.89 for a jet velocity of 132.96 m/s [436.2 ft/sec]. Aqueous solutions of CMC and PAM gave similar results. The hatched areas in Figs. 1 through 3 are drawn according to Tollmien in Ref. 9. The two borderlines are extreme cases given by Tollmien. It can be seen that the pressure attenuation can be described by Tolimien's equation only when the jet velocity is low and the nozzle size is small. Tollimien's equation is vc 0.96=Vn CL/rn where vc = jet velocity at centerline, m/s, vn = jet velocity at nozzle exit, m/s, L = jet distance (distance from nozzle to bottom), mm, c = experimental constant (c=0.066 to 0.076), and rn = nozzle radius, mm. Influence of Jet Nozzle Size on Pressure Attenuation. Cone Shaped Small Nozzles. It was found that with a similar jet velocity, the larger the nozzle, the slower the attenuation. Fig. 4 shows the experimental results without crossflow measured by the Pitot tube with the jet velocity ranging from 80.2 to 93.28 m/s [263.1 to 306 ft/sec]. With the same jet distance, pc/pn, increases as the diameter increases, although the jet velocity decreases. For example, when L/dn, = 10, pc/pn, =0.582, 0.809, and 0.849 for the diameters of 2.80, 3.74, and 4.85 mm [0.11, 0.15, and 0.19 in.], respectively. SPEDE P. 69^

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