Here, the feasibility of Neumann series expansion of Maxwell’s equations in the electrostatic limit is investigated for potentially rapid and approximate subsurface imaging of geologic features proximal to metallic infrastructure in an oilfield environment. While generally useful for efficient modeling of mild conductivity perturbations in uncluttered settings, we raise the question of its suitability for situations, such as oilfield, where metallic artifacts are pervasive, and in some cases, in direct electrical contact with the conductivity perturbation on which the Neumann series is computed. Convergence of the Neumann series and its residual error are computed using the hierarchical finite element framework for a canonical oilfield model consisting of an “L” shaped, steel-cased well, energized by a steady state electrode, and penetrating a small set of mildly conducting fractures near the heel of the well. For a given node spacing h in the finite element mesh, we find that the Neumann series is ultimately convergent if the conductivity is small enough - a result consistent with previous presumptions on the necessity of small conductivity perturbations. However, we also demonstrate that the spectral radius of the Neumann series operator grows as ~ 1/h, thus suggesting that in the limit of the continuous problem h → 0, the Neumann series is intrinsically divergent for all conductivity perturbation, regardless of their smallness. The hierarchical finite element methodology itself is critically analyzed and shown to possess the h2 error convergence of traditional linear finite elements, thereby supporting the conclusion of an inescapably divergent Neumann series for this benchmark example. Application of the Neumann series to oilfield problems with metallic clutter should therefore be done with careful consideration to the coupling between infrastructure and geology. Here, the methods used here are demonstrably useful in such circumstances.
Nanocrystalline metals offer significant improvements in structural performance over conventional alloys. However, their performance is limited by grain boundary instability and limited ductility. Solute segregation has been proposed as a stabilization mechanism, however the solute atoms can embrittle grain boundaries and further degrade the toughness. In the present study, we confirm the embrittling effect of solute segregation in Pt–Au alloys. However, more importantly, we show that inhomogeneous chemical segregation to the grain boundary can lead to a new toughening mechanism termed compositional crack arrest. Energy dissipation is facilitated by the formation of nanocrack networks formed when cracks arrested at regions of the grain boundaries that were starved in the embrittling element. This mechanism, in concert with triple junction crack arrest, provides pathways to optimize both thermal stability and energy dissipation. A combination of in situ tensile deformation experiments and molecular dynamics simulations elucidate both the embrittling and toughening processes that can occur as a function of solute content.
Accurate and efficient constitutive modeling remains a cornerstone issue for solid mechanics analysis. Over the years, the LAMÉ advanced material model library has grown to address this challenge by implementing models capable of describing material systems spanning soft polymers to stiff ceramics including both isotropic and anisotropic responses. Inelastic behaviors including (visco)plasticity, damage, and fracture have all incorporated for use in various analyses. This multitude of options and flexibility, however, comes at the cost of many capabilities, features, and responses and the ensuing complexity in the resulting implementation. Therefore, to enhance confidence and enable the utilization of the LAMÉ library in application, this effort seeks to document and verify the various models in the LAMÉ library. Specifically, the broader strategy, organization, and interface of the library itself is first presented. The physical theory, numerical implementation, and user guide for a large set of models is then discussed. Importantly, a number of verification tests are performed with each model to not only have confidence in the model itself but also highlight some important response characteristics and features that may be of interest to end-users. Finally, in looking ahead to the future, approaches to add material models to this library and further expand the capabilities are presented.
We study connections between the alternating direction method of multipliers (ADMM), the classical method of multipliers (MM), and progressive hedging (PH). The connections are used to derive benchmark metrics and strategies to monitor and accelerate convergence and to help explain why ADMM and PH are capable of solving complex nonconvex NLPs. Specifically, we observe that ADMM is an inexact version of MM and approaches its performance when multiple coordination steps are performed. In addition, we use the observation that PH is a specialization of ADMM and borrow Lyapunov function and primal-dual feasibility metrics used in ADMM to explain why PH is capable of solving nonconvex NLPs. This analysis also highlights that specialized PH schemes can be derived to tackle a wider range of stochastic programs and even other problem classes. Our exposition is tutorial in nature and seeks to to motivate algorithmic improvements and new decomposition strategies
This report presents a specification for the Portals 4 network programming interface. Portals 4 is intended to allow scalable, high-performance network communication between nodes of a parallel computing system. Portals 4 is well suited to massively parallel processing and embedded systems. Portals 4 represents an adaption of the data movement layer developed for massively parallel processing platforms, such as the 4500-node Intel TeraFLOPS machine. Sandia's Cplant cluster project motivated the development of Version 3.0, which was later extended to Version 3.3 as part of the Cray Red Storm machine and XT line. Version 4 is targeted to the next generation of machines employing advanced network interface architectures that support enhanced offload capabilities.