Tips for implementing multigrid methods on domains containing holes

As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised regions), via the multigrid method. We consider as a test case the Poisson equation with a nonlinear term added, as a means of illustrating the principles involved, and move to a "real world" 3-dimensional problem which is the solution of the conformally flat Hamiltonian constraint with Dirichlet and Robin boundary conditions. Using our vertex-centered multigrid code, we demonstrate globally second-order-accurate solutions of elliptic equations over domains containing holes, in two and three spatial dimensions. Keys to the success of this method are the choice of the restriction operator near the holes and definition of the location of the inner boundary. In some cases (e.g. two holes in two dimensions), more and more smoothing may be required as the mesh spacing decreases to zero; however for the resolutions currently of interest to many numerical relativists, it is feasible to maintain second order convergence by concentrating smoothing (spatially) where it is needed most. This paper, and our publicly available source code, are intended to serve as semi-pedagogical guides for those who may wish to implement similar schemes.Comment: 18 pages, 11 figures, LaTeX. Added clarifications and references re. scope of paper, mathematical foundations, relevance of work. Accepted for publication in Classical & Quantum Gravit

Per- and poly-fluoroalkyl substances (PFASs) in follicular fluid from women experiencing infertility in Australia

Per- and poly-fluoroalkyl substances (PFASs) have been widely used and detected in human matrices. Evidence that PFAS exposure may be associated with adverse human reproductive health effects exists, however, data is limited. The use of a human matrix such as follicular fluid to determine chemical exposure, along with reproductive data will be used to investigate if there is a relationship between PFAS exposure and human fertility. Objective: This study aims to: (1) assess if associations exist between PFAS concentrations and/or age and fertilisation rate (as determined in follicular fluid of women in Australia who received assisted reproductive treatment (ART)); and (2) assess if associations exist between PFAS concentrations and infertility aetiology. Methods: Follicular fluids were originally collected from participants who underwent fully stimulated ART treatment cycles at an in vitro fertilisation (IVF) clinic in the period 2006–2009 and 2010–11 in Queensland, Australia. The samples were available for analysis of 32 PFASs including perfluorooctane sulfonate (PFOS), perfluorooctanoic acid (PFOA), perfluorohexane sulfonate (PFHxS), and perfluorononanoic acid (PFNA) using high performance liquid chromatography tandem mass spectrometry (HPLC-MS/MS). 97 samples were matched with limited demographic data (age and fertilisation rate) and five infertility factors (three known female factors): 1) endometriosis, 2) polycystic ovarian syndrome (PCOS), and 3) genital tract infections - tubal/pelvic inflammation disease; as well as 4) male factor, and 5) idiopathic or unknown from either males or females. SPSS was used for linear regression analysis. Results: PFASs were detected in all follicular fluid samples with the mean concentrations of PFOS and PFOA, 4.9, and 2.4 ng/ml, respectively. A lower fertilisation rate was observed at higher age when age was added as a covariate, but there was no relationship between PFAS concentrations and fertilisation rate. There were few statistically significant associations between PFAS concentrations in follicular fluid and infertility factors. Log-transformed PFHxS concentrations were lower in females with endometriosis (factor 1) than in women who had reported ‘male factors’ as a reason of infertility, while PFHpA was higher in women who had infertile due to female factors (factor 1–3) compared to those who had infertile due to male factor. Conclusion: PFASs were detected in follicular fluid of Australian women who had been treated at an IVF clinic. PFAS exposure found in follicular fluids is linked to increased risk of some infertility factors, and increased age was associated with decreased fertilisation rate in our data. But there was no relationship between PFAS and ferlitisation rate. Further large-scale investigations of PFAS and health effects including infertility are warranted

PARALLEL COMPUTING: Fundamentals, Applications and New Directions

This volume gives an overview of the state-of-the-art with respect to the development of all types of parallel computers and their application to a wide range of problem areas. The international conference on parallel computing ParCo97 (Parallel Computing 97) was held in Bonn, Germany from 19 to 22 September 1997. The first conference in this biannual series was held in 1983 in Berlin. Further conferences were held in Leiden (The Netherlands), London (UK), Grenoble (France) and Gent (Belgium). From the outset the aim with the ParCo (Parallel Computing) conferences was to promote the application of parallel computers to solve real life problems. In the case of ParCo97 a new milestone was reached in that more than half of the papers and posters presented were concerned with application aspects. This fact reflects the coming of age of parallel computing. Some 200 papers were submitted to the Program Committee by authors from all over the world. The final programme consisted of four invited papers, 71 contributed scientific/industrial papers and 45 posters. In addition a panel discussion on Parallel Computing and the Evolution of Cyberspace was held. During and after the conference all final contributions were refereed. Only those papers and posters accepted during this final screening process are included in this volume. The practical emphasis of the conference was accentuated by an industrial exhibition where companies demonstrated the newest developments in parallel processing equipment and software. Speakers from participating companies presented papers in industrial sessions in which new developments in parallel computing were reported

Benefits of SMT and of Parallel Transpose Algorithm for the Large-Scale GYSELA Application

International audienceThis article describes how we manage to increase performance and to extend features of a large parallel application through the use of simultaneous multithreading (SMT) and by designing a robust parallel transpose algorithm. The semi-Lagrangian code Gysela typically performs large physics simulations using a few thousands of cores, between 1k cores up to 16k on x86-based clusters. However, simulations with finer resolutions and with kinetic electrons increase those needs by a huge factor, providing a good example of applications requiring Exascale machines. To improve Gysela compute times, we take advantage of efficient SMT implementations available on recent INTEL architectures. We also analyze the cost of a transposition communication scheme that involves a large number of cores in our case. Adaptation of the code for balance load whenever using both SMT and good deployment strategy led to a significant reduction that can be up to 38% of the execution times