A Parallel Structured Divide-and-Conquer Algorithm for Symmetric Tridiagonal Eigenvalue Problems

© 2021 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] In this article, a parallel structured divide-and-conquer (PSDC) eigensolver is proposed for symmetric tridiagonal matrices based on ScaLAPACK and a parallel structured matrix multiplication algorithm, called PSMMA. Computing the eigenvectors via matrix-matrix multiplications is the most computationally expensive part of the divide-and-conquer algorithm, and one of the matrices involved in such multiplications is a rank-structured Cauchy-like matrix. By exploiting this particular property, PSMMA constructs the local matrices by using generators of Cauchy-like matrices without any communication, and further reduces the computation costs by using a structured low-rank approximation algorithm. Thus, both the communication and computation costs are reduced. Experimental results show that both PSMMA and PSDC are highly scalable and scale to 4096 processes at least. PSDC has better scalability than PHDC that was proposed in [16] and only scaled to 300 processes for the same matrices. Comparing with PDSTEDC in ScaLAPACK, PSDC is always faster and achieves 1.4x-1.6x speedup for some matrices with few deflations. PSDC is also comparable with ELPA, with PSDC being faster than ELPA when using few processes and a little slower when using many processes.The authors would like to thank the referees for their valuable comments which greatly improve the presentation of this article. This work was supported by National Natural Science Foundation of China (No. NNW2019ZT6-B20, NNW2019ZT6B21, NNW2019ZT5-A10, U1611261, 61872392, and U1811461), National Key RD Program of China (2018YFB0204303), NSF of Hunan (No. 2019JJ40339), NSF of NUDT (No. ZK18-03-01), Guangdong Natural Science Foundation (2018B030312002), and the Program for Guangdong Introducing Innovative and Entrepreneurial Teams under Grant 2016ZT06D211. The work of Jose E. Roman was supported by the Spanish Agencia Estatal de Investigacion (AEI) under project SLEPc-DA (PID2019-107379RB-I00).Liao, X.; Li, S.; Lu, Y.; Román Moltó, JE. (2021). A Parallel Structured Divide-and-Conquer Algorithm for Symmetric Tridiagonal Eigenvalue Problems. IEEE Transactions on Parallel and Distributed Systems. 32(2):367-378. https://doi.org/10.1109/TPDS.2020.3019471S36737832

Study on Lubrication Characteristics of Metal Liquid Film Based on Electromagnetic-Elastic Mechanics-Hydrodynamics Multiphysics Coupling Model

In an electromagnetic rail launcher, a metal liquid film is created at the armature/rail (A/R) contact interface. It has a significant impact on electromagnetic launch performance. In this paper, an electromagnetic-elastic mechanics-hydrodynamics multi physics coupling model is established in consideration of the metal liquid film’s own acceleration, magnetic pressure and dynamic changes in film thickness. Based on this model, the lubricating characteristics of magnetic pressure and fluid pressure distribution, film thickness distribution and velocity distribution of the metal liquid film were studied. When the velocity of the metal liquid film is very fast, and the magnetic pressure is reduced, it may fail to maintain stability and rupture, which may be an important reason for the transition. Finally, this paper analyzes the lubrication effect of the metal liquid film, and points out that when we want strictly to control the muzzle velocity, the lubrication effect of the metal liquid film must be considered

Achieving Good Protection on Ultra-High Molecular Weight Polythene by In Situ Growth of Amorphous Carbon Film

Ultra-high molecular weight polythene (UHMWPE), with outstanding characteristics, is widely applied in modern industry, while it is also severely limited by its inherent shortcomings, which include low hardness, poor wear resistance, and easy wear. Implementation of feasible protection on ultra-high molecular weight polythene to overcome its shortcomings would be of significance. In the present study, amorphous carbon (a-C) film was fabricated on ultra-high molecular weight polythene (UHMWPE) to provide good protection, and the relevant growth mechanism of a-C film was revealed by controlling carbon plasma currents. The results showed the in situ transition layer, in the form of chemical bonds, was formed between the UHMWPE substrate and the a-C film with the introduction of carbon plasma, which provided strong adhesion, and then the a-C film continued epitaxial growth on the in situ transition layer with the treatment of carbon plasma. This in situ growth of a-C film, including the in situ transition layer and the epitaxial growth layer, significantly improved the wetting properties, mechanical properties, and tribological properties of UHMWPE. In particular, good protection by in situ growth a-C film on UHMWPE was achieved during sliding wear

Effects of different proportions of stevia stalk on nutrient utilization and rumen fermentation in ruminal fluid derived from sheep

Background Stevia straw is a byproduct of sugar crop stevia. It is a good feed material because of richness in nutrients and active substances (steviosides and flavonoids). However, due to improper utilization such as piling, burning and so on, it became a large amount of wasted straw resources and lead to environmental pollution. Methods We added 0%, 0.2%, 0.4%, 0.6%, 0.8%, 1.0% and 1.5% of stevia stalk to study the effects of different stevia stalk concentrations on nutrient utilization and rumen fermentation in sheep (based on sheep diet). In vitro fermentation method was used, with 17 repetitions for each treatment. All fermentation substrate based on sheep diet with different stevia stalk concentrations were fermented for 2 h, 6 h, 12 h, 24 h and 48 h, then the gas production, dry matter degradability (DMD), crude protein degradability (CPD), neutral detergent fiber degradability (NDFD), acid detergent fiber degradability (ADFD), pH, ammonia nitrogen (NH3-N) and volatile fatty acids (VFAs) were determined. Results The results showed that at different fermentation time, the change trend of gas production in each teatment was basically same, but the maximum occurred in 1.0% treatment at 48 h. The DMD, CPD, NDFD and ADFD of sheep diets increased with fermentation time increasing, especially the CPD48h, NDFD48h and ADFD48h of diets in 0.8%, 1.0% and 1.5% treatments were significantly higher than those in control (P 0.8% >1.5% >0.4% >0.6% >0.2%. Overall, 1.0% stevia stalk could promote nutrient degradation and sheep rumen fermentation

Effects of Isochlorogenic Acid on Ewes Rumen Fermentation, Microbial Diversity and Ewes Immunity of Different Physiological Stages

The effects of isochlorogenic acid (ICGA) on ewes rumen environment, microbial diversity, and immunity at different physiological stages (estrus, pregnancy and lactation) were studied in this experiment. Twenty healthy female Hu lambs of 1.5 months with similar body weight (17.82 ± 0.98 kg) and body condition were selected and randomly divided into two groups: the control group (CON) and the ICGA group (ICGA). The lambs of CON were fed a basal diet, while the lambs of ICGA were supplemented with 0.1% ICGA based on the basal diet. Lambs rumen fermentation characteristics, microbial diversity and immunity at estrus, pregnancy, and lactation stages were determined and analyzed, respectively. The results showed that the rumen pH in CON increased first and then decreased as lambs grew (p 3-N) showed the highest at estrus stage in both groups, but it was significantly higher in ICGA than that in CON (p p p p > 0.05). Principal component analysis (PCA) showed that there were significant differences in rumen microorganism structure between CON and ICGA at all physiological stages (p Firmicutes relative abundance of three physiological stages decreased (p > 0.05) while Bacteroidota increased (p > 0.05). The relative abundance of Synergistota at estrus stage and Patescibacteria at the lactation stage increased significantly too (p Prevotella at three stages showed the highest (p > 0.05), while the relative abundance of Succiniclasticum, unclassified_Selenomonadaceae and Rikenellaceae_RC9_gut_group showed different abundances at different physiological stages in ICGA. Compared with the CON, the lambs of the ICGA showed higher blood IgG, IgM, and TNF- α contents at three physiological stages and higher IL-6 contents at pregnancy stage (p 3-N at estrus, VFAs at pregnancy, and the ratio of A/P at lactation. It optimizes rumen microbial flora of different physiological stages by increasing Bacteroidota relative abundance while reducing Firmicutes relative abundance, maintaining rumen microbial homeostasis at pregnant stage, increasing the number of beneficial bacteria in later lactating and ewes blood immunoglobulins content at three physiological stages