MPI+X: task-based parallelization and dynamic load balance of finite element assembly

The main computing tasks of a finite element code(FE) for solving partial differential equations (PDE's) are the algebraic system assembly and the iterative solver. This work focuses on the first task, in the context of a hybrid MPI+X paradigm. Although we will describe algorithms in the FE context, a similar strategy can be straightforwardly applied to other discretization methods, like the finite volume method. The matrix assembly consists of a loop over the elements of the MPI partition to compute element matrices and right-hand sides and their assemblies in the local system to each MPI partition. In a MPI+X hybrid parallelism context, X has consisted traditionally of loop parallelism using OpenMP. Several strategies have been proposed in the literature to implement this loop parallelism, like coloring or substructuring techniques to circumvent the race condition that appears when assembling the element system into the local system. The main drawback of the first technique is the decrease of the IPC due to bad spatial locality. The second technique avoids this issue but requires extensive changes in the implementation, which can be cumbersome when several element loops should be treated. We propose an alternative, based on the task parallelism of the element loop using some extensions to the OpenMP programming model. The taskification of the assembly solves both aforementioned problems. In addition, dynamic load balance will be applied using the DLB library, especially efficient in the presence of hybrid meshes, where the relative costs of the different elements is impossible to estimate a priori. This paper presents the proposed methodology, its implementation and its validation through the solution of large computational mechanics problems up to 16k cores

FaMIDAS: A Mixed Frequency Factor Model with MIDAS structure

In this paper a dynamic factor model with mixed frequency is proposed (FaMIDAS), where the past observations of high frequency indicators are used following the MIDAS approach. This structure is able to represent with richer dynamics the information content of the economic indicators and produces smoothed factors and forecasts. In addition, it is particularly suited for real time forecast as it reduces the problem of the unbalanced data set and of the revisions in preliminary data. In the empirical application we specify and estimate a FaMIDAS to forecast Italian quarterly GDP. The short-term forecasting performance is evaluated against other mixed frequency models in a pseudo-real time experiment, also allowing for pooled forecast from factor models.Mixed frequency models, Dynamic factor Models, MIDAS, Forecasting

The bias-extension test for the analysis of in-plane shear properties of textile composite reinforcements and prepregs: a review

The bias-extension test is a rather simple experiment aiming to determine in-plane shear properties of textile composite reinforcements. However the mechanics during the test involves fibrous material at large shear strains and large rotations of the fibres. Several aspects are still being studied and are not yet modeled in a consensual manner. The standard analysis of the test is based on two assumptions: inextensibility of the fibers and rotations at the yarn crossovers without slippage. They lead to the development of zones with constant fibre orientations proper to the bias-extension test. Beyond the analysis of the test within these basic assumptions, the paper presents studies that have been carried out on the lack of verification of these hypothesis (slippage, tension in the yarns, effects of fibre bending). The effects of temperature, mesoscopic modeling and tension locking are also considered in the case of the bias-extension test

Stochastic Continuous Time Neurite Branching Models with Tree and Segment Dependent Rates

In this paper we introduce a continuous time stochastic neurite branching model closely related to the discrete time stochastic BES-model. The discrete time BES-model is underlying current attempts to simulate cortical development, but is difficult to analyze. The new continuous time formulation facilitates analytical treatment thus allowing us to examine the structure of the model more closely. We derive explicit expressions for the time dependent probabilities p(\gamma, t) for finding a tree \gamma at time t, valid for arbitrary continuous time branching models with tree and segment dependent branching rates. We show, for the specific case of the continuous time BES-model, that as expected from our model formulation, the sums needed to evaluate expectation values of functions of the terminal segment number \mu(f(n),t) do not depend on the distribution of the total branching probability over the terminal segments. In addition, we derive a system of differential equations for the probabilities p(n,t) of finding n terminal segments at time t. For the continuous BES-model, this system of differential equations gives direct numerical access to functions only depending on the number of terminal segments, and we use this to evaluate the development of the mean and standard deviation of the number of terminal segments at a time t. For comparison we discuss two cases where mean and variance of the number of terminal segments are exactly solvable. Then we discuss the numerical evaluation of the S-dependence of the solutions for the continuous time BES-model. The numerical results show clearly that higher S values, i.e. values such that more proximal terminal segments have higher branching rates than more distal terminal segments, lead to more symmetrical trees as measured by three tree symmetry indicators.Comment: 41 pages, 2 figures, revised structure and text improvement