Publications

Results 101–150 of 254
Skip to search filters

Fault Resilient Domain Decomposition Preconditioner for PDEs

Sargsyan, Khachik S.; Sargsyan, Khachik S.; Safta, Cosmin S.; Safta, Cosmin S.; Debusschere, Bert D.; Debusschere, Bert D.; Najm, H.N.; Najm, H.N.; Rizzi, Francesco N.; Rizzi, Francesco N.; Morris Wright, Karla V.; Morris Wright, Karla V.; Mycek, Paul M.; Mycek, Paul M.; Maitre, Olivier L.; Maitre, Olivier L.; Knio, Omar K.; Knio, Omar K.

The move towards extreme-scale computing platforms challenges scientific simula- tions in many ways. Given the recent tendencies in computer architecture development, one needs to reformulate legacy codes in order to cope with large amounts of commu- nication, system faults and requirements of low-memory usage per core. In this work, we develop a novel framework for solving partial differential equa- tions (PDEs) via domain decomposition that reformulates the solution as a state-of- knowledge with a probabilistic interpretation. Such reformulation allows resiliency with respect to potential faults without having to apply fault detection, avoids unnecessary communication and is generally well-positioned for rigorous uncertainty quantification studies that target improvements of predictive fidelity of scientific models. We demon- strate our algorithm for one-dimensional PDE examples where artificial faults have been implemented as bit-flips in the binary representation of subdomain solutions. *Sandia National Laboratories, 7011 East Ave, MS 9051, Livermore, CA 94550 (ksargsy@sandia.gov). t Sandia National Laboratories, Livermore, CA (fnrizzi@sandia.gov). IDuke University, Durham, NC (paul .mycek@duke . edu). Sandia National Laboratories, Livermore, CA (csaft a@sandia.gov). i llSandia National Laboratories, Livermore, CA (knmorri@sandia.gov). II Sandia National Laboratories, Livermore, CA (hnnajm@sandia.gov). **Laboratoire d'Informatique pour la Mecanique et les Sciences de l'Ingenieur, Orsay, France (olm@limsi . f r). ttDuke University, Durham, NC (omar . knio@duke . edu). It Sandia National Laboratories, Livermore, CA (bjdebus@sandia.gov).

More Details
TYPE SAND Report YEAR 2015
OSTIDOI

Hybrid discrete/continuum algorithms for stochastic reaction networks

Journal of Computational Physics

Safta, Cosmin S.; Sargsyan, Khachik S.; Debusschere, Bert D.; Najm, H.N.

Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. The performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.

More Details
TYPE Journal Article YEAR 2015
ScopusOSTIDOI

Probabilistic methods for sensitivity analysis and calibration in the NASA challenge problem

Journal of Aerospace Information Systems

Safta, Cosmin S.; Sargsyan, Khachik S.; Najm, H.N.; Chowdhary, Kenny; Debusschere, Bert D.; Swiler, Laura P.; Eldred, Michael S.

In this paper, a series of algorithms are proposed to address the problems in the NASA Langley Research Center Multidisciplinary Uncertainty Quantification Challenge. A Bayesian approach is employed to characterize and calibrate the epistemic parameters based on the available data, whereas a variance-based global sensitivity analysis is used to rank the epistemic and aleatory model parameters. A nested sampling of the aleatory-epistemic space is proposed to propagate uncertainties from model parameters to output quantities of interest.

More Details
TYPE Journal Article YEAR 2015
ScopusOSTIDOI

Rexsss Performance Analysis: Domain Decomposition Algorithm Implementations for Resilient Numerical Partial Differential Equation Solvers

Dahlgren, Kathryn M.; Rizzi, Francesco N.; Morris Wright, Karla V.; Debusschere, Bert D.

The future of extreme-scale computing is expected to magnify the influence of soft faults as a source of inaccuracy or failure in solutions obtained from distributed parallel computations. The development of resilient computational tools represents an essential recourse for understanding the best methods for absorbing the impacts of soft faults without sacrificing solution accuracy. The Rexsss (Resilient Extreme Scale Scientific Simulations) project pursues the development of fault resilient algorithms for solving partial differential equations (PDEs) on distributed systems. Performance analyses of current algorithm implementations assist in the identification of runtime inefficiencies.

More Details
TYPE Other Report YEAR 2014
OSTIDOI

UQTk version 2.0 user manual

Debusschere, Bert D.; Sargsyan, Khachik S.; Safta, Cosmin S.

The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 2.0 ffers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

More Details
TYPE SAND Report YEAR 2013
OSTIDOI

Fundamental issues in the representation and propagation of uncertain equation of state information in shock hydrodynamics

Computers and Fluids

Robinson, Allen C.; Berry, Robert D.; Carpenter, John H.; Debusschere, Bert D.; Drake, Richard R.; Mattsson, A.E.; Rider, William J.

Uncertainty quantification (UQ) deals with providing reasonable estimates of the uncertainties associated with an engineering model and propagating them to final engineering quantities of interest. We present a conceptual UQ framework for the case of shock hydrodynamics with Euler's equations where the uncertainties are assumed to lie principally in the equation of state (EOS). In this paper we consider experimental data as providing both data and an estimate of data uncertainty. We propose a specific Bayesian inference approach for characterizing EOS uncertainty in thermodynamic phase space. We show how this approach provides a natural and efficient methodology for transferring data uncertainty to engineering outputs through an EOS representation that understands and deals consistently with parameter correlations as sensed in the data.Historically, complex multiphase EOSs have been built utilizing tables as the delivery mechanism in order to amortize the cost of creation of the tables over many subsequent continuum scale runs. Once UQ enters into the picture, however, the proper operational paradigm for multiphase tables become much less clear. Using a simple single-phase Mie-Grüneisen model we experiment with several approaches and demonstrate how uncertainty can be represented. We also show how the quality of the tabular representation is of key importance. As a first step, we demonstrate a particular tabular approach for the Mie-Grüneisen model which when extended to multiphase tables should have value for designing a UQ-enabled shock hydrodynamic modeling approach that is not only theoretically sound but also robust, useful, and acceptable to the modeling community. We also propose an approach to separate data uncertainty from modeling error in the EOS. © 2012 Elsevier Ltd.

More Details
TYPE Conference YEAR 2013
ScopusOSTI
Results 101–150 of 254
Results 101–150 of 254