Publications

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The solution of the governing steady transport equations for momentum, heat and mass transfer in fluids undergoing non-equilibrium chemical reactions can be extremely challenging. The difficulties arise from both the complexity of the nonlinear solution behavior as well as the nonlinear, coupled, non-symmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this paper, we briefly review progress on developing a stabilized finite element (FE) capability for numerical solution of these challenging problems. The discussion considers the stabilized FE formulation for the low Mach number Navier-Stokes equations with heat and mass transport with non-equilibrium chemical reactions, and the solution methods necessary for detailed analysis of these complex systems. The solution algorithms include robust nonlinear and linear solution schemes, parameter continuation methods, and linear stability analysis techniques. Our discussion considers computational efficiency, scalability, and some implementation issues of the solution methods. Computational results are presented for a CFD benchmark problem as well as for a number of large-scale, 2D and 3D, engineering transport/reaction applications.

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As current experimental and simulation methods cannot determine the mobility of flat boundaries across the large misorientation phase space, we have developed a computational method for imposing an artificial driving force on boundaries. In a molecular dynamics simulation, this allows us to go beyond the inherent timescale restrictions of the technique and induce non-negligible motion in flat boundaries of arbitrary misorientation. For different series of symmetric boundaries, we find both expected and unexpected results. In general, mobility increases as the grain boundary plane deviates from (111), but high-coincidence and low-angle boundaries represent special cases. These results agree with and enrich experimental observations.

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While it had been known for a long time how to transform an asymmetric traveling salesman (ATS) problem on the complete graph with n vertices into a symmetric traveling salesman (STS) problem on an incomplete graph with 2n vertices, no method was available for using this correspondence to derive facets of the symmetric polytope from facets of the asymmetric polytope until the work of E. Balas and M. Fischetti in [Lifted cycle inequalities for the asymmetric traveling salesman problem, Mathematics of Operations Research 24 (2) (1999) 273-292] suggested an approach. The original Balas-Fischetti method uses a standard sequential lifting procedure for the computation of the coefficient of the edges that are missing in the incomplete STS graph, which is a difficult task when addressing classes of (as opposed to single) inequalities. In this paper we introduce a systematic procedure for accomplishing the lifting task. The procedure exploits the structure of the tight STS tours and organizes them into a suitable tree structure. The potential of the method is illustrated by deriving large new classes of facet-defining STS inequalities.

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Combinatorial algorithms have long played a pivotal enabling role in many applications of parallel computing. Graph algorithms in particular arise in load balancing, scheduling, mapping and many other aspects of the parallelization of irregular applications. These are still active research areas, mostly due to evolving computational techniques and rapidly changing computational platforms. But the relationship between parallel computing and discrete algorithms is much richer than the mere use of graph algorithms to support the parallelization of traditional scientific computations. Important, emerging areas of science are fundamentally discrete, and they are increasingly reliant on the power of parallel computing. Examples include computational biology, scientific data mining, and network analysis. These applications are changing the relationship between discrete algorithms and parallel computing. In addition to their traditional role as enablers of high performance, combinatorial algorithms are now customers for parallel computing. New parallelization techniques for combinatorial algorithms need to be developed to support these nontraditional scientific approaches. This chapter will describe some of the many areas of intersection between discrete algorithms and parallel scientific computing. Due to space limitations, this chapter is not a comprehensive survey, but rather an introduction to a diverse set of techniques and applications with a particular emphasis on work presented at the Eleventh SIAM Conference on Parallel Processing for Scientific Computing. Some topics highly relevant to this chapter (e.g. load balancing) are addressed elsewhere in this book, and so we will not discuss them here.

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In this article we describe stress nets, a technique for exploring 2D tensor fields. Our method allows a user to examine simultaneously the tensors eigenvectors (both major and minor) as well as scalar-valued tensor invariants. By avoiding noise-advection techniques, we are able to display both principal directions of the tensor field as well as the derived scalars without cluttering the display. We present a CPU-only implementation of stress nets as well as a hybrid CPU/GPU approach and discuss the relative strengths and weaknesses of each. Stress nets have been used as part of an investigation into crack propagation. They were used to display the directions of maximum shear in a slab of material under tension as well as the magnitude of the shear forces acting on each point. Our methods allowed users to find new features in the data that were not visible on standard plots of tensor invariants. These features disagree with commonly accepted analytical crack propagation solutions and have sparked renewed investigation. Though developed for a materials mechanics problem, our method applies equally well to any 2D tensor field having unique characteristic directions.

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Empirical studies suggest that consumption is more sensitive to current income than suggested under the permanent income hypothesis, which raises questions regarding expectations for future income, risk aversion, and the role of economic confidence measures. This report surveys a body of fundamental economic literature as well as burgeoning computational modeling methods to support efforts to better anticipate cascading economic responses to terrorist threats and attacks. This is a three part survey to support the incorporation of models of economic confidence into agent-based microeconomic simulations. We first review broad underlying economic principles related to this topic. We then review the economic principle of confidence and related empirical studies. Finally, we provide a brief survey of efforts and publications related to agent-based economic simulation.

Simulations within density functional theory (DFT) are a common component of research into the physics of materials. With the broad success of DFT, it is easily forgotten that computational DFT methods invariably do not directly represent simulated properties, but require careful construction of models that are computable approximations to a physical property. Perhaps foremost among these computational considerations is the routine use of the supercell approximation to construct finite models to represent infinite systems. Pitfalls in using supercells (k-space sampling, boundary conditions, cell sizes) are often underappreciated. We present examples (e.g. vacancy defects) that exhibit a surprising or significant dependence on supercells, and describe workable solutions. We describe procedures needed to construct meaningful models for simulations of real material systems, focusing on k-space and cell size issues.

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We propose a new class of Discontinuous Galerkin (DG) methods based on variational multiscale ideas. Our approach begins with an additive decomposition of the discontinuous finite element space into continuous (coarse) and discontinuous (fine) components. Variational multiscale analysis is used to define an interscale transfer operator that associates coarse and fine scale functions. Composition of this operator with a donor DG method yields a new formulation that combines the advantages of DG methods with the attractive and more efficient computational structure of a continuous Galerkin method. The new class of DG methods is illustrated for a scalar advection-diffusion problem.