Publications

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Meshfree methods are commonly applied to discretize peridynamic models, particularly in numerical simulations of engineering problems. Such methods discretize peridynamic bodies using a set of nodes with characteristic volume, leading to particle-based descriptions of systems. In this paper, we perform convergence studies of static peridynamic problems. We show that commonly used meshfree methods in peridynamics suffer from accuracy and convergence issues, due to a rough approximation of the contribution of nodes near the boundary of the neighborhood of a given node to numerical integrations. We propose two methods to improve meshfree peridynamic simulations. The first method uses accurate computations of volumes of intersections between neighbor cells and the neighborhood of a given node, referred to as partial volumes. The second method employs smooth influence functions with a finite support within peridynamic kernels. Numerical results demonstrate great improvements in accuracy and convergence of peridynamic numerical solutions when using the proposed methods.

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Concern is growing in the high-performance computing (HPC) community on the reliability of future extreme- scale systems. Current efforts have focused on appli- cation fault-tolerance rather than the operating system (OS), despite the fact that recent studies have suggested that failures in OS memory may be more likely. The OS is critical to a system's correct and efficient operation of the node and processes it governs-and the parallel na- ture of HPC applications means any single node failure generally forces all processes of this application to ter- minate due to tight communication in HPC. Therefore, the OS itself must be capable of tolerating failures in a robust system. In this work, we introduce mini-ckpts, a framework which enables application survival despite the occurrence of a fatal OS failure or crash. minickpts achieves this tolerance by ensuring that the crit- ical data describing a process is preserved in persistent memory prior to the failure. Following the failure, the OS is rejuvenated via a warm reboot and the applica- tion continues execution effectively making the failure and restart transparent. The mini-ckpts rejuvenation and recovery process is measured to take between three to six seconds and has a failure-free overhead of between 3-5% for a number of key HPC workloads. In contrast to current fault-tolerance methods, this work ensures that the operating and runtime systems can continue in the presence of faults. This is a much finer-grained and dynamic method of fault-tolerance than the current coarse-grained application-centric methods. Handling faults at this level has the potential to greatly reduce overheads and enables mitigation of additional faults.

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The computational solution of the governing balance equations for mass, momentum, heat transfer and magnetic induction for resistive magnetohydrodynamics (MHD) systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fully-implicit stabilized unstructured finite element (FE) capability for 3D incompressible resistive MHD. The discussion considers the development of a stabilized FE formulation in context of the variational multiscale (VMS) method, and describes the scalable implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton-Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, that include MHD duct flows, an unstable hydromagnetic Kelvin-Helmholtz shear layer, and a 3D island coalescence problem used to model magnetic reconnection. Initial results that explore the scaling of the solution methods are also presented on up to 128K processors for problems with up to 1.8B unknowns on a CrayXK7.

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We develop and analyze an optimization-based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. When some assumptions on the kernel functions hold, we prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia’s agile software components toolkit. As a result, the latter provides the groundwork for the development of engineering analysis tools, while numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method.

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