Advanced Newton Methods for Geodynamical Models of Stokes Flow with Viscoplastic Rheologies

Strain localization and resulting plasticity and failure play an important role in the evolution of the lithosphere. These phenomena are commonly modeled by Stokes flows with viscoplastic rheologies. The nonlinearities of these rheologies make the numerical solution of the resulting systems challenging, and iterative methods often converge slowly or not at all. Yet accurate solutions are critical for representing the physics. Moreover, for some rheology laws, aspects of solvability are still unknown. We study a basic but representative viscoplastic rheology law. The law involves a yield stress that is independent of the dynamic pressure, referred to as von Mises yield criterion. Two commonly used variants, perfect/ideal and composite viscoplasticity, are compared. We derive both variants from energy minimization principles, and we use this perspective to argue when solutions are unique. We propose a new stress-velocity Newton solution algorithm that treats the stress as an independent variable during the Newton linearization but requires solution only of Stokes systems that are of the usual velocity-pressure form. To study different solution algorithms, we implement 2D and 3D finite element discretizations, and we generate Stokes problems with up to 7 orders of magnitude viscosity contrasts, in which compression or tension results in significant nonlinear localization effects. Comparing the performance of the proposed Newton method with the standard Newton method and the Picard fixed-point method, we observe a significant reduction in the number of iterations and improved stability with respect to problem nonlinearity, mesh refinement, and the polynomial order of the discretization.Comment: To appear in Geochemistry, Geophysics, Geosystem

Robust and efficient primal-dual Newton-Krylov solvers for viscous-plastic sea-ice models

We present a Newton-Krylov solver for a viscous-plastic sea-ice model. This constitutive relation is commonly used in climate models to describe the material properties of sea ice. Due to the strong nonlinearity introduced by the material law in the momentum equation, the development of fast, robust and scalable solvers is still a substantial challenge. In this paper, we propose a novel primal-dual Newton linearization for the implicitly-in-time discretized momentum equation. Compared to existing methods, it converges faster and more robustly with respect to mesh refinement, and thus enables numerically converged sea-ice simulations at high resolutions. Combined with an algebraic multigrid-preconditioned Krylov method for the linearized systems, which contain strongly varying coefficients, the resulting solver scales well and can be used in parallel. We present experiments for two challenging test problems and study solver performance for problems with up to 8.4 million spatial unknowns.Comment: 18 pages, 7 figure

EFFECT OF EIGHT WEEKS VIBRATION TRAINING ON THE LOWER LIMB BASIC ABILITY AND ATHLETIC PERFORMANCE OF GYMNASTS

The purpose of this study explores the effects of 8 weeks vibration training on the basic ability (explosive power, speed, agility) and athletic performance (backward somersault) of the lower limbs of gymnasts. Sixteen gymnasts were randomly divided into vibration training group (VT) and control group (CON). Participants were trained for eight weeks and performed countermovement jump (CMJ), sprints, shuttle run, and backward somersault tests before the training, after 4 weeks, and 8 weeks of training. The significant level was set to α = .05. The results showed that the speed of VT increased significantly after 4 weeks of training, and the speed and agility of VT increased significantly after 8 weeks of training (p \u3c.05). In conclusion, Gymnasts can improve their speed ability through 4 weeks of vibration training, and 8 weeks vibration training can improve their speed and agility

Correlation of Morphology and In-Vitro Degradation Behavior of Spray Pyrolyzed Bioactive Glasses

Bioactive glass (BG) is considered to be one of the Most remarkable Materials in the field of bone tissue regeneration due to its superior bioactivity. In this study, both un-treated and polyethylene glycols (PEG)-treated BG particles were prepared using a spray pyrolysis process to study the correlation between particle Morphology and degradation behavior. The phase compositions, surface Morphologies, inner structures, and specific surface areas of all BG specimens were examined by X-ray diffraction, scanning electron Microscopy, transmission electron Microscopy, and nitrogen adsorption/desorption, respectively. Simulated body fluid (SBF) immersion evaluated the assessments of bioactivity and degradation behavior. The results demonstrate three particle Morphologies of solid, porous, and hollow factors. The correlation between porosity, bioactivity, and degradation behavior was discussed