A Nonoverlapping Domain Decomposition Method for Incompressible Stokes Equations with Continuous Pressures

This is the publisher's version, also available electronically from http://epubs.siam.org/doi/abs/10.1137/120861503A nonoverlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the proposed algorithm, Lagrange multipliers are used to enforce continuity of the velocity component across the subdomain boundary. The continuity of the pressure component is enforced in the primal form, i.e., neighboring subdomains share the same pressure degrees of freedom on the subdomain interface and no Lagrange multipliers are needed. After eliminating all velocity variables and the independent subdomain interior parts of the pressures, a symmetric positive semidefinite linear system for the subdomain boundary pressures and the Lagrange multipliers is formed and solved by a preconditioned conjugate gradient method. A lumped preconditioner is studied and the condition number bound of the preconditioned operator is proved to be independent of the number of subdomains for fixed subdomain problem size. Numerical experiments demonstrate the convergence rate of the proposed algorithm

A FETI-DP TYPE DOMAIN DECOMPOSITION ALGORITHM FOR THREE-DIMENSIONAL INCOMPRESSIBLE STOKES EQUATIONS

The FETI-DP (dual-primal finite element tearing and interconnecting) algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp. 1235–1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp. 128–149] for solving incompressible Stokes equations, are extended to three-dimensional problems. A new analysis of the condition number bound for using the Dirichlet preconditioner is given. The algorithm and analysis are valid for mixed finite elements with both continuous and discontinuous pressures. An advantage of this new analysis is that the numerous coarse level velocity components, required in the previous analysis to enforce the divergence-free subdomain boundary velocity conditions, are no longer needed. This greatly reduces the size of the coarse level problem in the algorithm, especially for three-dimensional problems. The coarse level velocity space can be chosen as simple as those coarse spaces for solving scalar elliptic problems corresponding to each velocity component. Both the Dirichlet and lumped preconditioners are analyzed using the same framework in this new analysis. Their condition number bounds are proved to be independent of the number of subdomains for fixed subdomain problem size. Numerical experiments in both two and three dimensions, using mixed finite elements with both continuous and discontinuous pressures, demonstrate the convergence rate of the algorithms

Synchronization of Memristive FitzHugh-Nagumo Neural Networks

A new mathematical model of neural networks described by diffusive FitzHugh-Nagumo equations with memristors and linear synaptic coupling is proposed and investigated. The existence of absorbing set for the solution semiflow in the energy space is proved and global dynamics of the memristive neural networks are dissipative. Through uniform estimates and maneuver of integral inequalities on the interneuron difference equations, it is shown that exponential synchronization of the neural network at a uniform convergence rate occurs if the coupling strength satisfies a threshold condition explicitly expressed by the system parameters, which is illustrated by an example and numerical simulation experiments.Comment: arXiv admin note: text overlap with arXiv:2209.0194

Digital economy, spatial spillover and carbon intensity: concurrently on the threshold effect of human capital

Under the new development pattern, green low-carbon and digital economy become two mainstream development directions in China. Against the background ‘dual carbon’ strategies, based on the data of China between 2010 and 2018 at the city level, The paper adopts dynamic spatial Durbin models to investigate the causal links causal between digital economy and carbon intensity by constructing different spatial weight matrices, and explore the influence of human capital with threshold model. Results show that：(1) Urban digital economy and carbon intensity show significant positive spatial correlation characteristics. The carbon reduction of digital economy has obvious spatial spillover effect under different spatial weight matrices. (2) Industrial structure upgrading, technological innovation and resource allocation optimization are effective channels through which digital economy contributes to carbon emission reduction. (3) A doublethreshold effect of human capital is evident in the carbon reduction of digital economy. The findings offer new perspectives and empirical evidence for understanding the causality relation between the digital economy and carbon emission, and those conclusions have important policy implications for how to promote the digital economy development and thus achieve the ‘double carbon goal’

Genetically engineered pre-microRNA-34a prodrug suppresses orthotopic osteosarcoma xenograft tumor growth via the induction of apoptosis and cell cycle arrest.

Osteosarcoma (OS) is the most common primary malignant bone tumor in children, and microRNA-34a (miR-34a) replacement therapy represents a new treatment strategy. This study was to define the effectiveness and safety profiles of a novel bioengineered miR-34a prodrug in orthotopic OS xenograft tumor mouse model. Highly purified pre-miR-34a prodrug significantly inhibited the proliferation of human 143B and MG-63 cells in a dose dependent manner and to much greater degrees than controls, which was attributed to induction of apoptosis and G2 cell cycle arrest. Inhibition of OS cell growth and invasion were associated with release of high levels of mature miR-34a from pre-miR-34a prodrug and consequently reduction of protein levels of many miR-34a target genes including SIRT1, BCL2, c-MET, and CDK6. Furthermore, intravenous administration of in vivo-jetPEI formulated miR-34a prodrug significantly reduced OS tumor growth in orthotopic xenograft mouse models. In addition, mouse blood chemistry profiles indicated that therapeutic doses of bioengineered miR-34a prodrug were well tolerated in these animals. The results demonstrated that bioengineered miR-34a prodrug was effective to control OS tumor growth which involved the induction of apoptosis and cell cycle arrest, supporting the development of bioengineered RNAs as a novel class of large molecule therapeutic agents