A factored sparse approximate inverse preconditioned conjugate gradient solver on graphics processing units

Graphics Processing Units (GPUs) exhibit significantly higher peak performance than conventional CPUs. However, in general only highly parallel algorithms can exploit their potential. In this scenario, the iterative solution to sparse linear systems of equations could be carried out quite efficiently on a GPU as it requires only matrix-by-vector products, dot products, and vector updates. However, to be really effective, any iterative solver needs to be properly preconditioned and this represents a major bottleneck for a successful GPU implementation. Due to its inherent parallelism, the factored sparse approximate inverse (FSAI) preconditioner represents an optimal candidate for the conjugate gradient-like solution of sparse linear systems. However, its GPU implementation requires a nontrivial recasting of multiple computational steps. We present our GPU version of the FSAI preconditioner along with a set of results that show how a noticeable speedup with respect to a highly tuned CPU counterpart is obtained

A robust adaptive algebraic multigrid linear solver for structural mechanics

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming kernel in commercial simulators; thus, it is of significant interest the development of robust and efficient linear solvers for such applications. In this context, direct solvers, which are based on LU factorization techniques, are often used due to their robustness and easy setup; however, they can reach only superlinear complexity, in the best case, thus, have limited applicability depending on the problem size. On the other hand, iterative solvers based on algebraic multigrid (AMG) preconditioners can reach up to linear complexity for sufficiently regular problems but do not always converge and require more knowledge from the user for an efficient setup. In this work, we present an adaptive AMG method specifically designed to improve its usability and efficiency in the solution of structural problems. We show numerical results for several practical applications with millions of unknowns and compare our method with two state-of-the-art linear solvers proving its efficiency and robustness.Comment: 50 pages, 16 figures, submitted to CMAM

A Novel Factorized Sparse Approximate Inverse Preconditioner with Supernodes

AbstractKrylov methods preconditioned by Factorized Sparse Approximate Inverses (FSAI) are an efficient approach for the solution of symmetric positive definite linear systems on massively parallel computers. However, FSAI often suffers from a high set-up cost, especially in ill-conditioned problems. In this communication we propose a novel algorithm for the FSAI computation that makes use of the concept of supernode borrowed from sparse LU factorizations and direct methods

A robust multilevel approximate inverse preconditioner for symmetric positive definite matrices

The use of factorized sparse approximate inverse (FSAI) preconditioners in a standard multilevel framework for symmetric positive definite (SPD) matrices may pose a number of issues as to the definiteness of the Schur complement at each level. The present work introduces a robust multilevel approach for SPD problems based on FSAI preconditioning, which eliminates the chance of algorithmic breakdowns independently of the preconditioner sparsity. The multilevel FSAI algorithm is further enhanced by introducing descending and ascending low-rank corrections, thus giving rise to the multilevel FSAI with low-rank corrections (MFLR) preconditioner. The proposed algorithm is investigated in a number of test problems. The numerical results show that the MFLR preconditioner is a robust approach that can significantly accelerate the solver convergence rate preserving a good degree of parallelism. The possibly large set-up cost, mainly due to the computation of the eigenpairs needed by low-rank corrections, makes its use attractive in applications where the preconditioner can be recycled along a number of linear solves

A novel methodological approach for land subsidence prediction through data assimilation techniques

AbstractAnthropogenic land subsidence can be evaluated and predicted by numerical models, which are often built over deterministic analyses. However, uncertainties and approximations are present, as in any other modeling activity of real-world phenomena. This study aims at combining data assimilation techniques with a physically-based numerical model of anthropogenic land subsidence in a novel and comprehensive workflow, to overcome the main limitations concerning the way traditional deterministic analyses use the available measurements. The proposed methodology allows to reduce uncertainties affecting the model, identify the most appropriate rock constitutive behavior and characterize the most significant governing geomechanical parameters. The proposed methodological approach has been applied in a synthetic test case representative of the Upper Adriatic basin, Italy. The integration of data assimilation techniques into geomechanical modeling appears to be a useful and effective tool for a more reliable study of anthropogenic land subsidence

A General-Purpose AMG Linear Solver for High Performance Computing

The numerical simulation of modern engineering problems via finite elements requires the solution of sparse linear systems of millions or even billions of unknowns. The algebraic multigrid (AMG) methods are the most common choice as linear solvers because of their fast convergence even for large-size problems. In this communication, we propose Chronos, a massively parallel implementation of a novel AMG framework, specifically designed to address complex problems by adapting its components, from the smoother, to the coarse grid correction and prolongation to the problem at hand. This work demonstrates not only the numerical performance of the proposed library, but also its robustness and adaptability to very challenging matrices, arising from different fields of application

Immunoreactive trypsinogen levels in newborn screened infants with an inconclusive diagnosis of cystic fibrosis.

BACKGROUND: Newborn screening (NBS) for cystic fibrosis (CF) not only identifies infants with a diagnosis of CF, but also those with an uncertain diagnosis of cystic fibrosis (CF), i.e. CF transmembrane conductance regulator (CFTR)-related metabolic syndrome (CRMS) or CF screen positive inconclusive diagnosis (CFSPID). These infants have an uncertain long-term outcome and it is currently unclear around time of diagnosis, which infants are at higher risk of later fulfilling a CF diagnosis. In this study, we hypothesised that immunoreactive trypsinogen (IRT) levels, used in NBS as a marker of pancreatic disease and function, may reflect the degree of CFTR dysfunction in each individual and therefore would help to identify those with CRMS/CSPID who are later at risk for meeting the criteria of CF. METHODS: In this longitudinal, prospective study, infants with CRMS/CFSPID and CF were recruited and followed in 9 CF clinics (Canada and Italy). We compared NBS IRT levels between CF and CRMS/CFSPID, and between children with CRMS/CFSPID→CF and CRMS/CFSPID→CRMS/CFSPID during the period of June 2007 to April 2016. RESULTS: Ninety eight CRMS/CFSPID and 120 CF subjects were enrolled. During the study period, 14 (14.3%) CRMS/CFSPID subjects fulfilled the diagnostic criteria for CF (CRMS/CFSPID→CF), while the diagnosis remained uncertain (CRMS/CFSPID→ CRMS/CFSPID) in 84 (85.7%) subjects. Significantly higher NBS IRT concentrations (ng/ml) were present in CF than CRMS/CFPSID (median (interquartile range): 143.8 (99.8-206.2) vs. 75.0 (61.0-105.9); P \u3c 0.0001). Infants with CRMS/CFSPID→CF (n = 14) had significantly higher NBS IRT concentrations (ng/ml) than CRMS/CFSPID→ CRMS/CFSPID (n = 83) (median (interquartile range): 108.9 (72.3-126.8) vs. 73.7(60.0-96.0); P = 0.02). CONCLUSIONS: Amongst infants who tested positive on NBS for CF, there is a gradation of elevated NBS IRT concentrations. Infants with CF have higher NBS IRT levels than CRMS/CFPSID, and higher NBS IRT concentrations were present in infants with CRMS/CFSPID→CF than CRMS/CFSPID→ CRMS/CFSPID. NBS IRT concentrations, in concert with other factors, may have the potential to predict the likelihood of CF amongst infants with CRMS/CFSPID

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements