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Debusschere, Bert

Publications and source records attributed to Debusschere, Bert.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Fault Resilient Domain Decomposition Preconditioner for PDEs

The move towards extreme-scale computing platforms challenges scientific simulations 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 communication, system faults and requirements of low-memory usage per core. In this work, we develop a novel framework for solving partial differential equations (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 demonstrate our algorithm for one-dimensional PDE examples where artificial faults have been implemented as bit-flips in the binary representation of subdomain solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Hybrid discrete/continuum algorithms for stochastic reaction networks

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.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

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

In this study, 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.

97 MATHEMATICS AND COMPUTING↗