Refined Isogeometric Analysis for a preconditioned conjugate gradient solver

Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces C 0 hyperplanes that act as separators for the direct LU factorization solver. As a result, the total computational cost required to solve the corresponding system of equations using a direct LU factorization solver dramatically reduces (up to a factor of 55) (Garcia et al., 2017). At the same time, rIGA enriches the IGA spaces, thus improving the best approximation error. In this work, we extend the complexity analysis of rIGA to the case of iterative solvers. We build an iterative solver as follows: we first construct the Schur complements using a direct solver over small subdomains (macro-elements). We then assemble those Schur complements into a global skeleton system. Subsequently, we solve this system iteratively using Conjugate Gradients (CG) with an incomplete LU (ILU) preconditioner. For a 2D Poisson model problem with a structured mesh and a uniform polynomial degree of approximation, rIGA achieves moderate savings with respect to IGA in terms of the number of Floating Point Operations (FLOPs) and computational time (in seconds) required to solve the resulting system of linear equations. For instance, for a mesh with four million elements and polynomial degree p=3, the iterative solver is approximately 2.6 times faster (in time) when applied to the rIGA system than to the IGA one. These savings occur because the skeleton rIGA system contains fewer non-zero entries than the IGA one. The opposite situation occurs for 3D problems, and as a result, 3D rIGA discretizations provide no gains with respect to their IGA counterparts when considering iterative solvers

Micropolar fluids using B-spline divergence conforming spaces

We discretized the two-dimensional linear momentum, microrotation, energy and mass conservation equations from micropolar fluids theory, with the finite element method, creating divergence conforming spaces based on B-spline basis functions to obtain pointwise divergence free solutions [8]. Weak boundary conditions were imposed using Nitsche's method for tangential conditions, while normal conditions were imposed strongly. Once the exact mass conservation was provided by the divergence free formulation, we focused on evaluating the differences between micropolar fluids and conventional fluids, to show the advantages of using the micropolar fluid model to capture the features of complex fluids. A square and an arc heat driven cavities were solved as test cases. A variation of the parameters of the model, along with the variation of Rayleigh number were performed for a better understanding of the system. The divergence free formulation was used to guarantee an accurate solution of the flow. This formulation was implemented using the framework PetIGA as a basis, using its parallel stuctures to achieve high scalability. The results of the square heat driven cavity test case are in good agreement with those reported earlier. © The Authors. Published by Elsevier B.V

On round-off error for adaptive finite element methods

Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called 'radical meshes'. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix. © 2012 Published by Elsevier Ltd

Effects of an early rehabilitation program for adult cystic fibrosis patients during hospitalization: a randomized clinical trial

There is little information on pulmonary rehabilitation in patients with cystic fibrosis (CF) with pulmonary exacerbation. This study aimed to evaluate the effects of an early rehabilitation program on lung function, muscle strength, inflammatory markers, and quality of life in adults with CF hospitalized for pulmonary exacerbation. In this randomized controlled trial, 19 patients were included in the intervention group and 15 in the control group. The intervention group underwent an early rehabilitation program for 14 days after admission. All patients underwent spirometry, one-repetition maximum tests (1RM), and the 6-min walk test, and answered the Revised Cystic Fibrosis Questionnaire (CFQ-R) for quality of life and the International Physical Activity Questionnaire. Serum levels of interleukin and tumor necrosis factor alpha (TNF-α) were measured. In the intervention group, there were increases in 1RM biceps (P=0.009), triceps (P=0.005), shoulder abductors (P=0.002), shoulder flexors (P=0.004), hamstrings (P<0.001), and quadriceps values (P<0.001). In addition, there were improvements in CFQ-R-emotion (P=0.002), treatment burden (P=0.002), vitality (P=0.011), and physical scores (P=0.026), and a reduction in the Borg resting fatigue score (P=0.037). The interleukins levels did not change after the intervention. In adult CF patients with pulmonary exacerbation, early hospital rehabilitation had a significant impact on improving resting fatigue, muscle strength, and quality of life

Cytoskeleton structure, pattern of mitochondrial activity and ultrastructure of frozen or vitrified sheep embryos.

Even though sheep embryo cryopreservation is a commonly used procedure the survival and pregnancy outcomes can vary greatly. This study investigated whether cryopreservation was causing subtle changes in ultrastructure, mitochondrial activity or cytoskeletal integrity. Sheep embryos were either slow cooled in 1.5 M EG (n = 22), or vitrified in 20% EG + 20% DMSO with 0.5 M sucrose in Open Pulled Straws (OPS) (n = 24). One hour after warming the cryopreserved embryos differed from control embryos in that they had no mitochondrial activity combined with cytoskeletal disorganization and large vesicles. Vitrified embryos also showed many points of cytoskeleton disruption. Ultrastructural alterations resulting from actin filaments disorganization were observed in both cryopreserved groups. This includes areas presenting no cytoplasmic organelles, Golgi complex located far from the nucleus and a decrease of specialized intercellular junctions. Additionally, large vesicles were observed in vitrified morulae and early blastocysts. The alterations after cryopreservation were proportional to embryo quality as assessed using the stereomicroscope. Even in the absence of mitochondrial activity, grade I and II cryopreserved embryos contained mitochondria with normal ultrastructure. Embryos classified as grade I or II in the stereomicroscope revealed mild ultrastructural alterations, meaning that this tool is efficient to evaluate embryos after cryopreservation

Telescopic hybrid fast solver for 3D elliptic problems with point singularities

This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver

Relationship between physical attributes and heat stress in dairy cattle from different genetic groups.

Dairy cattle raised under harsh conditions have to adapt and prevent heat stress. The aim of this study was to evaluate physical characteristics and their association with heat tolerance in different genetic groups of dairy cattle. Thickness of the skin and coat, length and number of hairs, body measurements, as well as physiological parameters and body temperatures by infrared thermography were determined in 19 Holstein and 19 Girolando (½ and ¾ Holstein) cows. The Holstein cattle were less tolerant to heat stress than Girolando (GH50 and GH75 Holstein), because of the difficulty in dissipating heat due to the larger body size, as well as thicker and longer hairs. The correlations between physical characteristics, physiological parameters, and thermographic measurements prove to be inconsistent among genetic groups and therefore are not predictive of heat tolerance, while the regressions of morphometric characteristics on physiological and thermographic measures were not significant. Thus, the physical characteristics were not good predictors of physiological indices and thermographic temperature and so should not be used

Relationship between physical attributes and heat stress in dairy cattle from different genetic groups.

Dairy cattle raised under harsh conditions have to adapt and prevent heat stress. The aim of this study was to evaluate physical characteristics and their association with heat tolerance in different genetic groups of dairy cattle. Thickness of the skin and coat, length and number of hairs, body measurements, as well as physiological parameters and body temperatures by infrared thermography were determined in 19 Holstein and 19 Girolando (½ and ¾ Holstein) cows. The Holstein cattle were less tolerant to heat stress than Girolando (GH50 and GH75 Holstein), because of the difficulty in dissipating heat due to the larger body size, as well as thicker and longer hairs. The correlations between physical characteristics, physiological parameters, and thermographic measurements prove to be inconsistent among genetic groups and therefore are not predictive of heat tolerance, while the regressions of morphometric characteristics on physiological and thermographic measures were not significant. Thus, the physical characteristics were not good predictors of physiological indices and thermographic temperature and so should not be used