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Algorithms and Abstractions for Assembly in PDE Codes: Workshop Report

Cyr, Eric C.; Phipps, Eric T.; Heroux, Michael A.; Brown, Jed; Coon, Ethan T.; Hoemmen, Mark F.; Kirby, Robert C.; Kolev, Tzanio V.; Sutherland, James C.; Trott, Christian R.

The emergence of high-concurrency architectures offering unprecedented performance has brought many high-performance partial differential equation (PDE) discretization codes to the precipice of a major refactor. To help address this challenge a workshop titled "Algorithms and Abstractions for Assembly in PDE Codes" was held in the Computer Science Research Institute at Sandia National Laboratories on May 12th-14th, 2014. This document summarizes the goals of the workshop and the results of the presentations and subsequent discussions.

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TYPE SAND Report YEAR 2014
DOIOSTI

Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies

Safta, Cosmin S.; Najm, H.N.; Phipps, Eric T.

Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.

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TYPE SAND Report YEAR 2014
DOIDOIOSTIOSTI

Exploring Heterogeneous Multicore Architectures for Advanced Embedded Uncertainty Quantification

Phipps, Eric T.; Edwards, Harold C.; Hu, Jonathan J.

We explore rearrangements of classical uncertainty quantification methods with the aim of achieving higher aggregate performance for uncertainty quantification calculations on emerging multicore and many core architectures. We show a rearrangement of the stochastic Galerkin method leads to improved performance and scalability on several computational architectures whereby uncertainty information is propagated at the lowest levels of the simulation code improving memory access patterns, exposing new dimensions of fine grained parallelism, and reducing communication. We also develop a general framework for implementing such rearrangements for a diverse set of uncertainty quantification algorithms as well as computational simulation codes to which they are applied.

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TYPE SAND Report YEAR 2014
DOIOSTI
Results 76–100 of 161
Results 76–100 of 161