Publications

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High explosives are an important class of energetic materials used in many weapons applications. Even with modern computers, the simulation of the dynamic chemical reactions and energy release is exceedingly challenging. While the scale of the detonation process may be macroscopic, the dynamic bond breaking responsible for the explosive release of energy is fundamentally quantum mechanical. Thus, any method that does not adequately describe bonding is destined to lack predictive capability on some level. Performing quantum mechanics calculations on systems with more than dozens of atoms is a gargantuan task, and severe approximation schemes must be employed in practical calculations. We have developed and tested a divide and conquer (DnC) scheme to obtain total energies, forces, and harmonic frequencies within semi-empirical quantum mechanics. The method is intended as an approximate but faster solution to the full problem and is possible due to the sparsity of the density matrix in many applications. The resulting total energy calculation scales linearly as the number of subsystems, and the method provides a path-forward to quantum mechanical simulations of millions of atoms.

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The optimization of sensor placements is a key aspect of the design of contaminant warning systems for automatically detecting contaminants in water distribution systems. Although researchers have generally assumed that all sensors are placed at the same time, in practice sensor networks will likely grow and evolve over time. For example, limitations for a water utility's budget may dictate an staged, incremental deployment of sensors over many years. We describe optimization formulations of multi-stage sensor placement problems. The objective of these formulations includes an explicit trade-off between the value of the initially deployed and final sensor networks. This trade-off motivates the deployment of sensors in initial stages of the deployment schedule, even though these choices typically lead to a solution that is suboptimal when compared to placing all sensors at once. These multi-stage sensor placement problems can be represented as mixed-integer programs, and we illustrate the impact of this trade-off using standard commercial solvers. We also describe a multi-stage formulation that models budget uncertainty, expressed as a tree of potential budget scenarios through time. Budget uncertainty is used to assess and hedge against risks due to a potentially incomplete deployment of a planned sensor network. This formulation is a multi-stage stochastic mixed-integer program, which are notoriously difficult to solve. We apply standard commercial solvers to small-scale test problems, enabling us to effectively analyze multi-stage sensor placement problems subject to budget uncertainties, and assess the impact of accounting for such uncertainty relative to a deterministic multi-stage model. © 2012 ASCE.

We present a mixed-integer linear programming formulation to determine optimal locations for manual grab sampling after the detection of contaminants in a water distribution system. The formulation selects optimal manual grab sample locations that maximize the total pair-wise distinguishability of candidate contamination events. Given an initial contaminant detection location, a source inversion is performed that will eliminate unlikely events resulting in a much smaller set of candidate contamination events. We then propose a cyclical process where optimal grab samples locations are determined and manual grab samples taken. Relying only on YES/NO indicators of the presence of contaminant, source inversion is performed to reduce the set of candidate contamination events. The process is repeated until the number of candidate events is sufficiently small. Case studies testing this process are presented using water network models ranging from 4 to approximately 13000 nodes. The results demonstrate that the contamination event can be identified within a remarkably small number of sampling cycles using very few sampling teams. Furthermore, solution times were reasonable making this formulation suitable for real-time settings. © 2012 ASCE.

A general-purpose algorithm for mesh optimization via node-movement, known as the Target-Matrix Paradigm, is introduced. The algorithm is general purpose in that it can be applied to a wide variety of mesh and element types, and to various commonly recurring mesh optimization problems such as shape improvement, and to more unusual problems like boundary-layer preservation with sliver removal, high-order mesh improvement, and edge-length equalization. The algorithm can be considered to be a direct optimization method in which weights are automatically constructed to enable definitions of application- specific mesh quality. The high-level concepts of the paradigm have been implemented in the Mesquite mesh improvement library, along with a number of concrete algorithms that address mesh quality issues such as those shown in the examples of the present paper. © Springer-Verlag (outside the USA) 2011.

Proposed exascale systems will present a number of considerable resiliency challenges. In particular, DRAM soft-errors, or bit-flips, are expected to greatly increase due to the increased memory density of these systems. Current hardware-based fault-tolerance methods will be unsuitable for addressing the expected soft error frequency rate. As a result, additional software will be needed to address this challenge. In this paper we introduce LIBSDC, a tunable, transparent silent data corruption detection and correction library for HPC applications. LIBSDC provides comprehensive SDC protection for program memory by implementing on-demand page integrity verification. Experimental benchmarks with Mantevo HPCCG show that once tuned, LIBSDC is able to achieve SDC protection with 50% overhead of resources, less than the 100% needed for double modular redundancy. © 2012 Springer-Verlag Berlin Heidelberg.

This study compares several block-oriented preconditioners for the stabilized finite element discretization of the incompressible Navier-Stokes equations. This includes standard additive Schwarz domain decomposition methods, aggressive coarsening multigrid, and three preconditioners based on an approximate block LU factorization, specifically SIMPLEC, LSC, and PCD. Robustness is considered with a particular focus on the impact that different stabilization methods have on preconditioner performance. Additionally, parallel scaling studies are undertaken. The numerical results indicate that aggressive coarsening multigrid, LSC and PCD all have good algorithmic scalability. Coupling this with the fact that block methods can be applied to systems arising from stable mixed discretizations implies that these techniques are a promising direction for developing scalable methods for Navier-Stokes. © 2011.