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Stability of Peridynamic Correspondence Material Models and Their Particle Discretizations

Silling, Stewart A.

Peridynamic correspondence material models provide a way to combine a material model from the local theory with the inherent capabilities of peridynamics to model long-range forces and fracture. However, correspondence models in a typical particle discretization suffer from zero-energy mode instability. These instabilities are shown here to be an aspect of material stability. A stability condition is derived for state-based materials starting from the requirement of potential energy minimization. It is shown that all correspondence materials fail this stability condition due to zero-energy deformation modes of the family. To eliminate these modes, a term is added to the correspondence strain energy density that resists deviations from a uniform deformation. The resulting material model satisfies the stability condition while effectively leaving the stress tensor unchanged. Computational examples demonstrate the effectiveness of the modified material model in avoiding zero-energy mode instability in a peridynamic particle code.

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TYPE SAND Report YEAR 2016
DOIOSTI

Enabling fast, stable and accurate peridynamic computations using multi-time-step integration

Computer Methods in Applied Mechanics and Engineering

Lindsay, Payton L.; Parks, Michael L.; Prakash, A.

Peridynamics is a nonlocal extension of classical continuum mechanics that is well-suited for solving problems with discontinuities such as cracks. This paper extends the peridynamic formulation to decompose a problem domain into a number of smaller overlapping subdomains and to enable the use of different time steps in different subdomains. This approach allows regions of interest to be isolated and solved at a small time step for increased accuracy while the rest of the problem domain can be solved at a larger time step for greater computational efficiency. Performance of the proposed method in terms of stability, accuracy, and computational cost is examined and several numerical examples are presented to corroborate the findings.

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TYPE Journal Article YEAR 2016
DOIOSTIScopus

Anti-persistence on persistent storage: History-independent sparse tables and dictionaries

Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems

Bender, Michael A.; Berry, Jonathan W.; Johnson, Rob; Kroeger, Thomas M.; Mccauley, Samuel; Phillips, Cynthia A.; Simon, Bertrand; Singh, Shikha; Zage, David J.

We present history-independent alternatives to a B-tree, the primary indexing data structure used in databases. A data structure is history independent (HI) if it is impossible to deduce any information by examining the bit representation of the data structure that is not already available through the API. We show how to build a history-independent cache-oblivious B-tree and a history-independent external-memory skip list. One of the main contributions is a data structure we build on the way - a history-independent packed-memory array (PMA). The PMA supports efficient range queries, one of the most important operations for answering database queries. Our HI PMA matches the asymptotic bounds of prior non-HI packed-memory arrays and sparse tables. Specifically, a PMA maintains a dynamic set of elements in sorted order in a linearsized array. Inserts and deletes take an amortized O(log2 N) element moves with high probability. Simple experiments with our implementation of HI PMAs corroborate our theoretical analysis. Comparisons to regular PMAs give preliminary indications that the practical cost of adding history-independence is not too large. Our HI cache-oblivious B-tree bounds match those of prior non-HI cache-oblivious B-trees. Searches take O(logB N) I/Os; inserts and deletes take O(log2N/B + logB N) amortized I/Os with high probability; and range queries returning k elements take O(logB N + k/B) I/Os. Our HI external-memory skip list achieves optimal bounds with high probability, analogous to in-memory skip lists: O(logB N) I/Os for point queries and amortized O(logB N) I/Os for inserts/deletes. Range queries returning k elements run in O(logB N + k/B) I/Os. In contrast, the best possible high-probability bounds for inserting into the folklore B-skip list, which promotes elements with probability 1/B, is just Θ(log N) I/Os. This is no better than the bounds one gets from running an inmemory skip list in external memory.

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TYPE Conference Poster YEAR 2016
DOIOSTIScopus

A cross-enclave composition mechanism for exascale system software

Proceedings of the 6th International Workshop on Runtime and Operating Systems for Supercomputers, ROSS 2016 - In conjunction with HPDC 2016

Evans, Noah; Laros, James H.; Kocoloski, Brian; Lange, John; Lang, Michael; Bridges, Patrick G.

As supercomputers move to exascale, the number of cores per node continues to increase, but the I/O bandwidth between nodes is increasing more slowly. This leads to computational power outstripping I/O bandwidth. This growth, in turn, encourages moving as much of an HPC workflow as possible onto the node in order to minimize data movement. One particular method of application composition, enclaves, co-locates different operating systems and runtimes on the same node where they communicate by in situ communication mechanisms. In this work, we describe a mechanism for communicating between composed applications. We implement a mechanism using Copy onWrite cooperating with XEMEM shared memory to provide consistent, implicitly unsynchronized communication across enclaves. We then evaluate this mechanism using a composed application and analytics between the Kitten Lightweight Kernel and Linux on top of the Hobbes Operating System and Runtime. These results show a 3% overhead compared to an application running in isolation, demonstrating the viability of this approach.

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TYPE Conference Poster YEAR 2016
DOIOSTIScopus

A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions

Computers and Mathematics with Applications

D'Elia, Marta D.; Perego, Mauro P.; Bochev, Pavel B.; Littlewood, David J.

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. 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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TYPE Conference Poster YEAR 2016
DOIOSTIScopus
Results 4651–4700 of 9,998
Results 4651–4700 of 9,998