PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of the underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.
This paper explores various frameworks to quantify and propagate sources of epistemic and aleatoric uncertainty within the context of decision making for assessing system performance relative to design margins of a complex mechanical system. If sufficient data is available for characterizing aleatoric-type uncertainties, probabilistic methods are commonly used for computing response distribution statistics based on input probability distribution specifications. Conversely, for epistemic uncertainties, data is generally too sparse to support objective probabilistic input descriptions, leading to either subjective probabilistic descriptions (e.g., assumed priors in Bayesian analysis) or non-probabilistic methods based on interval specifications. Among the techniques examined in this work are (1) Interval analysis, (2) Dempster-Shafer Theory of Evidence, (3) a second-order probability (SOP) analysis in which the aleatory and epistemic variables are treated separately, and a nested iteration is performed, typically sampling epistemic variables on the outer loop, then sampling over aleatory variables on the inner loop and (4) a Bayesian approach where plausible prior distributions describing the epistemic variable are created and updated using available experimental data. This paper compares the results and the information provided by different methods to enable decision making in the context of performance assessment when epistemic uncertainty is considered.
This paper discusses the handling and treatment of uncertainties corresponding to relatively few data samples in experimental characterization of random quantities. The importance of this topic extends beyond experimental uncertainty to situations where the derived experimental information is used for model validation or calibration. With very sparse data it is not practical to have a goal of accurately estimating the underlying variability distribution (probability density function, PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a desired percentage of the actual PDF, say 95% included probability, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the random-variable range corresponding to the desired percentage of the actual PDF. The performance of a variety of uncertainty representation techniques is tested and characterized in this paper according to these two opposing objectives. An initial set of test problems and results is presented here from a larger study currently underway.
With the increasing levels of parallelism in a compute node, it is important to exploit multiple levels of parallelism even within a single compute node. We present ShyLU (pro- nounced\Shy-loo"for Scalable Hybrid LU), a\hybrid-hybrid" solver for general sparse linear systems that is hybrid in two ways: First, it combines direct and iterative methods. The iterative method is based on approximate Schur com- plements. Second, the solver uses two levels of parallelism via hybrid programming (MPI+threads). Our solver is use- ful both in shared-memory environments and on large par- allel computers with distributed memory (as a subdomain solver). We compare the robustness of ShyLU against other algebraic preconditioners. ShyLU scales well up to 192 cores for a given problem size. We compare at MPI performance of ShyLU against a hybrid implementation. We conclude that on present multicore nodes at MPI is better. However, for future manycore machines (48 or more cores) hybrid/ hi- erarchical algorithms and implementations are important for sustained performance. Copyright is held by the author/owner(s).
We analyze the artificial dissipation introduced by a streamline-upwind Petrov-Galerkin finite element method and consider its effect on the conservation of total enthalpy for the Euler and laminar Navier-Stokes equations. We also consider the chemically reacting case. We demonstrate that in general, total enthalpy is not conserved for the important special case of the steady-state Euler equations. A modification to the artificial dissipation is proposed and shown to significantly improve the conservation of total enthalpy.
This presentation will discuss progress towards developing a large-scale parallel CFD capability using stabilized finite element formulations to simulate turbulent reacting flow and heat transfer in light water nuclear reactors (LWRs). Numerical simultation plays a critical role in the design, certification, and operation of LWRs. The Consortium for Advanced Simulation of Light Water Reactors is a U. S. Department of Energy Innovation Hub that is developing a virtual reactor toolkit that will incorporate science-based models, state-of-the-art numerical methods, modern computational science and engineering practices, and uncertainty quantification (UQ) and validation against operating pressurized water reactors. It will couple state-of-the-art fuel performance, neutronics, thermal-hydraulics (T-H), and structural models with existing tools for systems and safety analysis and will be designed for implementation on both today's leadership-class computers and next-generation advanced architecture platforms. We will first describe the finite element discretization utilizing PSPG, SUPG, and discontinuity capturing stabilization. We will then discuss our initial turbulence modeling formulations (LES and URANS) and the scalable fully implicit, fully coupled solution methods that are used to solve the challenging systems. These include globalized Newton-Krylov methods for solving the nonlinear systems of equaitons and preconditioned Krylov techniques. The preconditioners are based on fully-coupled algebraic multigrid and approximate block factorization preconditioners. We will discuss how these methods provide a powerful integration path for multiscale coupling to the neutronics and structures applications. Initial results on scalabiltiy will be presented. Finally we will comment on our use of embedded technology and how this capbaility impacts the application of implicit methods, sensitivity analysis and UQ.
Inference techniques play a central role in many cognitive systems. They transform low-level observations of the environment into high-level, actionable knowledge which then gets used by mechanisms that drive action, problem-solving, and learning. This paper presents an initial effort at combining results from AI and psychology into a pragmatic and scalable computational reasoning system. Our approach combines a numeric notion of plausibility with first-order logic to produce an incremental inference engine that is guided by heuristics derived from the psychological literature. We illustrate core ideas with detailed examples and discuss the advantages of the approach with respect to cognitive systems.
The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the DAKOTA software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of DAKOTA-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of DAKOTA's iterative analysis capabilities.
The objective of the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation Waste Integrated Performance and Safety Codes (NEAMS Waste IPSC) is to provide an integrated suite of computational modeling and simulation (M&S) capabilities to quantitatively assess the long-term performance of waste forms in the engineered and geologic environments of a radioactive-waste storage facility or disposal repository. Achieving the objective of modeling the performance of a disposal scenario requires describing processes involved in waste form degradation and radionuclide release at the subcontinuum scale, beginning with mechanistic descriptions of chemical reactions and chemical kinetics at the atomic scale, and upscaling into effective, validated constitutive models for input to high-fidelity continuum scale codes for coupled multiphysics simulations of release and transport. Verification and validation (V&V) is required throughout the system to establish evidence-based metrics for the level of confidence in M&S codes and capabilities, including at the subcontiunuum scale and the constitutive models they inform or generate. This Report outlines the nature of the V&V challenge at the subcontinuum scale, an approach to incorporate V&V concepts into subcontinuum scale modeling and simulation (M&S), and a plan to incrementally incorporate effective V&V into subcontinuum scale M&S destined for use in the NEAMS Waste IPSC work flow to meet requirements of quantitative confidence in the constitutive models informed by subcontinuum scale phenomena.
This is a companion publication to the paper 'A Matrix-Free Trust-Region SQP Algorithm for Equality Constrained Optimization' [11]. In [11], we develop and analyze a trust-region sequential quadratic programming (SQP) method that supports the matrix-free (iterative, in-exact) solution of linear systems. In this report, we document the numerical behavior of the algorithm applied to a variety of equality constrained optimization problems, with constraints given by partial differential equations (PDEs).
Graph algorithms are becoming increasingly important for solving many problems in scientific computing, data mining and other domains. As these problems grow in scale, parallel computing resources are required to meet their computational and memory requirements. Unfortunately, the algorithms, software, and hardware that have worked well for developing mainstream parallel scientific applications are not necessarily effective for large-scale graph problems. In this paper we present the inter-relationships between graph problems, software, and parallel hardware in the current state of the art and discuss how those issues present inherent challenges in solving large-scale graph problems. The range of these challenges suggests a research agenda for the development of scalable high-performance software for graph problems.