Construction of higher order accurate vortex and particle methods

The standard point vortex method has recently been shown to be of high order of accuracy for problems on the whole plane, when using a uniform initial subdivision for assigning the vorticity to the points. If obstacles are present in the flow, this high order deteriorates to first or second order. New vortex methods are introduced which are of arbitrary accuracy (under regularity assumptions) regardless of the presence of bodies and the uniformity of the initial subdivision

Analysis and convergence of the MAC scheme. Part 1: The linear problem

The MAC discretization of fluid flow is analyzed for the stationary Stokes equations. It is proved that the discrete approximations do in fact converge to the exact solutions of the flow equations. Estimates using mesh dependent norms analogous to the standard H(sup 1) and L(sup 2) norms are given for the velocity and pressure, respectively

Iterative methods for elliptic finite element equations on general meshes

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included

On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations

New discretization and solution techniques for incompressible viscous flow problems

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned

Prediction of small for gestational age neonates: screening by maternal factors, fetal biometry, and biomarkers at 35-37 weeks' gestation

Background: Small for gestational age (SGA) neonates are at increased risk of perinatal mortality and morbidity, but the risks can be substantially reduced if the condition is identified prenatally, because in such cases close monitoring and appropriate timing of delivery and prompt neonatal care can be undertaken. The traditional approach of identifying pregnancies with SGA fetuses is maternal abdominal palpation and serial measurements of symphysial-fundal height, but the detection rate of this approach is less than 30%. A higher performance of screening for SGA is achieved by sonographic fetal biometry during the third trimester; screening at 30-34 weeks’ gestation identifies about 80% of SGA neonates delivering preterm but only 50% of those delivering at term, at screen positive rate of 10%. There is some evidence that routine ultrasound examination at 36 weeks' gestation is more effective than that at 32 weeks in predicting birth of SGA neonates. Objective: To investigate the potential value of maternal characteristics and medical history, sonographycally estimated fetal weight (EFW) and biomarkers of impaired placentation at 35+0 - 36+6 weeks’ gestation in the prediction of delivery of small for gestational age (SGA) neonates. Methods: A dataset of 124,443 prospectively examined singleton pregnancies at 11+0 - 13+6 weeks’ gestation was used to derive, through multivariable logistic regression analysis, the patient-specific prior risk for delivery of SGA neonate with birthweight <10th percentile for gestational age from maternal characteristics and medical history. A dataset of 19,209 singleton pregnancies undergoing screening at 35+0 - 36+6 weeks’ gestation was divided into a training set and a validation set. The training dataset was used to develop models from multivariable logistic regression analysis to determine whether addition of uterine artery pulsatility index (UtA-PI), umbilical artery PI (UA-PI), fetal middle cerebral artery PI (MCA-PI), maternal serum placental growth factor (PlGF) and soluble fms-like tyrosine kinase-1 (sFLT) improved the performance of maternal factors and EFW in the prediction of delivery of SGA neonates. The models were then tested in the validation dataset to assess performance of screening. Results In the training dataset, in the SGA group, compared to those with birthweight ≥10th percentile, the median multiple of the median (MoM) values of PLGF and MCA-PI were reduced, whereas UtA-PI, UA-PI and sFLT were increased. Multivariable regression analysis demonstrated that in the prediction of SGA <10th there were significant contributions from maternal factors, EFW Z-score, UtA-PI MoM, MCA-PI MoM and PlGF MoM. In the validation dataset, prediction of 90% of SGA neonates delivering within two weeks of assessment was achieved by a screen positive rate of 67% in screening by maternal factors, 23% by maternal factors and EFW and 21% by the addition of biomarkers; the respective values for prediction of SGA neonates delivering at any stage after assessment were 66%, 32% and 30%. Conclusion: Addition of biomarkers of impaired placentation only marginally improves the predictive performance for delivery of SGA neonates achieved by maternal factors and fetal biometry at 35+0 - 36+6 weeks’ gestation

Prediction of small-for-gestational-age neonates at 35-37 weeks' gestation: contribution of maternal factors and growth velocity between 20 and 36 weeks

Objective: To evaluate the performance of ultrasonographic estimated fetal weight (EFW) at 35+0 - 36+6 weeks’ gestation in the prediction of small for gestational age (SGA) neonates and assess the additive value of first, maternal risk factors and second, fetal growth velocity between 20 and 36 weeks’ gestation in improving such prediction. Methods: This was a prospective study of 44,043 singleton pregnancies that had undergone routine ultrasound examination at 19+0 - 23+6 and at 35+0 - 36+6 weeks’ gestation. Multivariable logistic regression analysis was used to determine whether addition of maternal risk factors and growth velocity, defined by a difference in EFW Z-scores or fetal abdominal circumference (AC) Z-scores between the third and second trimester scans divided by the time interval between them, improved the performance of EFW at 35+0 - 36+6 weeks in the prediction of delivery of SGA neonates with birthweight <10th and <3rd percentiles within two weeks and at any stage after assessment. Results: Screening by EFW at 35+0 - 36+6 weeks’ gestation <10th percentile predicted 63.4% (95% CI 62.0, 64.7) of neonates with birthweight <10th percentile and 74.2% (95% CI 72.2, 76.1) of neonates with birthweight <3rd percentile born at any stage after assessment, at screen positive rate of 10%. The respective values for SGA neonates born within two weeks of assessment were 76.8% (95% CI 74.4, 79.0) and 81.3% (95% CI 78.2, 84.0). In the group of fetuses with EFW <10th percentile, 43.7% were born with birthweight ≥10th percentile. For a desired 90% detection rate of SGA neonates delivering at any stage after assessment the necessary screen positive rate would be 33.7% for SGA <10th percentile and 24.4% for SGA <3rd percentile. Multivariable logistic regression analysis demonstrated that in the prediction of SGA neonates with birthweight <10th and <3rd percentiles there was a significant contribution from EFW Z-score at 35+0 - 36+6 weeks’ gestation, maternal risk factors and AC growth velocity, but not EFW growth velocity. However, the area under the receiver operating characteristic curves for SGA neonates in screening by maternal risk factors and EFW Z-score was not improved by addition of AC growth velocity. Conclusion: Screening for SGA neonates by EFW at 35+0 - 36+6 weeks’ gestation and use of a cut-off of the 10th percentile predicts 63% of affected neonates. Prediction of 90% of SGA neonates necessitates classification of about 35% of the population as being screen positive use of the 35th percentile cut-off in EFW. The predictive performance of EFW is not improved by addition of estimated growth velocity between the second and third trimesters of pregnancy

Prediction of small-for-gestational-age neonates at 35-37 weeks' gestation: contribution of maternal factors and growth velocity between 32 and 36 weeks

Objective: To assess the additive value of fetal growth velocity between 32 and 36 weeks’ gestation on the performance of ultrasonographic estimated fetal weight (EFW) at 35+0 - 36+6 weeks’ gestation for prediction of small for gestational age (SGA) neonates and adverse perinatal outcome. Methods: This was a prospective study of 14,497 singleton pregnancies that had undergone routine ultrasound examination at 28+0 - 34+6 and at 35+0 - 36+6 weeks’ gestation. Multivariable logistic regression analysis was used to determine whether addition of growth velocity, defined by a difference in EFW and abdominal circumference (AC) Z-scores between the early and late third trimester scans divided by the time interval between them, improved the performance of EFW at 35+0 - 36+6 weeks in the prediction of first, delivery of SGA neonates with birthweight <10th and <3rd percentiles within two weeks and at any stage after assessment and second, composite of adverse perinatal outcome defined as stillbirth, neonatal death or admission to the neonatal unit for ≥48 hours. Results Multivariable logistic regression analysis demonstrated that significant contributors to prediction of SGA neonates were EFW Z-score at 35+0 - 36+6 weeks’ gestation, fetal growth velocity by either AC or EFW Z-scores and maternal risk factors. The area under the receiver operating characteristic curves (AUROC) and detection rate (DR) with 95% confidence interval, at 10% screen positive rate, for prediction of SGA neonates <10th percentile born within two weeks of assessment achieved by EFW Z-score at 35+0 - 36+6 weeks (AUROC 0.938, 0.928 - 0.947; DR 80.7, 77.6 - 83.9) were not significantly improved by addition of EFW growth velocity and maternal risk factors (AUROC 0.941, 0.932 - 0.950; p=0.061; DR 82.5, 79.4 - 85.3). Similar results were obtained when growth velocity was defined by AC rather than EFW growth velocity. Similarly, there was no significant improvement in AUROC and DR, at 10% screen positive rate, for prediction of SGA neonates <10th percentile born at any stage after assessment or SGA neonates <3rd percentile born within two weeks or at any stage after assessment achieved by EFW Z-score at 35+0 - 36+6 weeks by addition of maternal factors and either EFW growth velocity of AC growth velocity. Multivariable logistic regression analysis demonstrated that the only significant contributor to adverse perinatal outcome was maternal risk factors. Multivariable logistic regression analysis in the group with EFW <10th percentile demonstrated that significant contribution to prediction of birth of neonates with birthweight <10th and <3rd percentiles and adverse perinatal outcome was provided by EFW Z-score at 35+0 - 36+6 weeks, but not by AC growth velocity <1st decile. Conclusion: The predictive performance of EFW at 35+0 - 36+6 weeks’ gestation for birth of SGA neonates and adverse perinatal outcome is not improved by addition of estimated growth velocity between 32 and 36 weeks’ gestation

Covolume solutions of three dimensional div-curl equations

Delaunay-Voronoi mesh systems provide a generalization of the classical rectangular staggered meshes to unstructured meshes. It is shown how such 'covolume' discretizations may be applied to div-curl systems in three dimensions. Error estimates are proved and confirmed by a numerical illustration

Value of routine ultrasound examination at 35-37 weeks' gestation in diagnosis of fetal abnormalities

Objective: To investigate the potential value of routine ultrasound examination at 35-37 weeks’ gestation in the diagnosis of previously unknown fetal abnormalities. Methods: This was a prospective study in 52,401 singleton pregnancies attending for a routine ultrasound examination at 35+0 - 36+6 weeks’ gestation; all pregnancies had a previous scan at 18-24 weeks and 47,215 also had a scan at 11-13 weeks. We included pregnancies resulting in livebirth or stillbirth but excluded those with known chromosomal abnormalities. The abnormalities were classified according to affected major organ system and the type and incidence of new abnormalities was determined. Results: In the study population the incidence of fetal abnormalities was 2.2% (1,168 / 52,401), including 847 (72.5%) that had been previously diagnosed during the first and / or second trimester, 247 (21.2%) that were detected for the first time at 35-37 weeks and 74 (6.3%) that were detected for the first time postnatally. The most common abnormalities that were diagnosed during the first and / or second trimester, that were also observed at 35-37 weeks, included aberrant right subclavian artery, ventricular septal defect, talipes, unilateral renal agenesis and / or pelvic kidney, hydronephrosis, duplex kidney or unilateral multicystic kidney, cystic pulmonary airway malformation, ventriculomegaly, cleft lip and palate, polydactyly,abdominal cyst or gastroschisis. The most common abnormalities seen at 35-37 weeks were hydronephrosis, mild ventriculomegaly, ventricular septal defect, duplex kidney, ovarian cyst and arachnoid cyst. The incidence of abnormalities first seen at 35-37 weeks was 0.5% and the most common were ovarian cysts, microcephaly, achondroplasia, dacryocystocele and hematocolpos. The incidence of abnormalities first seen postnatally was 0.1% and the most common were isolated cleft palate, polydactyly or syndactyly and ambiguous genitalia or hypospadias; prenatal examination of the genitalia was not a compulsory part of the protocol. Conclusions: A high proportion of fetal abnormalities are detected for the first time during a routine ultrasound examination at 35-37 weeks’ gestation. Such diagnosis and subsequent management, including selection of time and place for delivery and postnatal investigations, could potentially improve postnatal outcome