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

Altimetry, gravimetry, GPS and viscoelastic modeling data for the joint inversion for glacial isostatic adjustment in Antarctica (ESA STSE Project REGINA)

The poorly known correction for the ongoing deformation of the solid Earth caused by glacial isostatic adjustment (GIA) is a major uncertainty in determining the mass balance of the Antarctic ice sheet from measurements of satellite gravimetry and to a lesser extent satellite altimetry. In the past decade, much progress has been made in consistently modeling ice sheet and solid Earth interactions; however, forward-modeling solutions of GIA in Antarctica remain uncertain due to the sparsity of constraints on the ice sheet evolution, as well as the Earth's rheological properties. An alternative approach towards estimating GIA is the joint inversion of multiple satellite data – namely, satellite gravimetry, satellite altimetry and GPS, which reflect, with different sensitivities, trends in recent glacial changes and GIA. Crucial to the success of this approach is the accuracy of the space-geodetic data sets. Here, we present reprocessed rates of surface-ice elevation change (Envisat/Ice, Cloud,and land Elevation Satellite, ICESat; 2003–2009), gravity field change (Gravity Recovery and Climate Experiment, GRACE; 2003–2009) and bedrock uplift (GPS; 1995–2013). The data analysis is complemented by the forward modeling of viscoelastic response functions to disc load forcing, allowing us to relate GIA-induced surface displacements with gravity changes for different rheological parameters of the solid Earth. The data and modeling results presented here are available in the PANGAEA database (https://doi.org/10.1594/PANGAEA.875745). The data sets are the input streams for the joint inversion estimate of present-day ice-mass change and GIA, focusing on Antarctica. However, the methods, code and data provided in this paper can be used to solve other problems, such as volume balances of the Antarctic ice sheet, or can be applied to other geographical regions in the case of the viscoelastic response functions. This paper presents the first of two contributions summarizing the work carried out within a European Space Agency funded study: Regional glacial isostatic adjustment and CryoSat elevation rate corrections in Antarctica (REGINA)

hp-adaptive discontinuous Galerkin solver for elliptic equations in numerical relativity

A considerable amount of attention has been given to discontinuous Galerkin methods for hyperbolic problems in numerical relativity, showing potential advantages of the methods in dealing with hydrodynamical shocks and other discontinuities. This paper investigates discontinuous Galerkin methods for the solution of elliptic problems in numerical relativity. We present a novel hp-adaptive numerical scheme for curvilinear and non-conforming meshes. It uses a multigrid preconditioner with a Chebyshev or Schwarz smoother to create a very scalable discontinuous Galerkin code on generic domains. The code employs compactification to move the outer boundary near spatial infinity. We explore the properties of the code on some test problems, including one mimicking Neutron stars with phase transitions. We also apply it to construct initial data for two or three black holes

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive manufacturing requires highly-accurate multiscale and multiphysics analyses. Only high performance computing tools are able to handle such complexity in time frames compatible with time-to-market. However, efficiency, without loss of accuracy, has rarely held the centre stage in the numerical community. Here, in contrast, the framework is designed to adequately exploit the resources of high-end distributed-memory machines. It is grounded on three building blocks: (1) Hierarchical adaptive mesh refinement with octree-based meshes; (2) a parallel strategy to model the growth of the geometry; (3) state-of-the-art parallel iterative linear solvers. Computational experiments consider the heat transfer analysis at the part scale of the printing process by powder-bed technologies. After verification against a 3D benchmark, a strong-scaling analysis assesses performance and identifies major sources of parallel overhead. A third numerical example examines the efficiency and robustness of (2) in a curved 3D shape. Unprecedented parallelism and scalability were achieved in this work. Hence, this framework contributes to take on higher complexity and/or accuracy, not only of part-scale simulations of metal or polymer additive manufacturing, but also in welding, sedimentation, atherosclerosis, or any other physical problem where the physical domain of interest grows in time

Context-Aware Handover Policies in HetNets

Next generation cellular systems are expected to entail a wide variety of wireless coverage zones, with cells of different sizes and capacities that can overlap in space and share the transmission resources. In this scenario, which is referred to as Heterogeneous Networks (HetNets), a fundamental challenge is the management of the handover process between macro, femto and pico cells. To limit the number of handovers and the signaling between the cells, it will hence be crucial to manage the user's mobility considering the context parameters, such as cells size, traffic loads, and user velocity. In this paper, we propose a theoretical model to characterize the performance of a mobile user in a HetNet scenario as a function of the user's mobility, the power profile of the neighboring cells, the handover parameters, and the traffic load of the different cells. We propose a Markov-based framework to model the handover process for the mobile user, and derive an optimal context-dependent handover criterion. The mathematical model is validated by means of simulations, comparing the performance of our strategy with conventional handover optimization techniques in different scenarios. Finally, we show the impact of the handover regulation on the users performance and how it is possible to improve the users capacity exploiting context information