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The analysis of a sparse grid stochastic collocation method for partial differential equations with high-dimensional random input data

Webster, Clayton G.

This work describes the convergence analysis of a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms (input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite elements, corresponding to a deterministic set of points in the random input space. This naturally requires solving uncoupled deterministic problems and, as such, the derived strong error estimates for the fully discrete solution are used to compare the computational efficiency of the proposed method with the Monte Carlo method. Numerical examples illustrate the theoretical results and are used to compare this approach with several others, including the standard Monte Carlo.

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TYPE SAND Report YEAR 2007
DOIOSTI

Lagrangian continuum dynamics in ALEGRA

Love, Edward L.; Wong, Michael K.

Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.

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TYPE SAND Report YEAR 2007
DOIOSTI

Low-Altitude Airbursts and the Impact Threat - Final LDRD Report

Boslough, Mark B.; Crawford, D.A.

The purpose of this nine-week project was to advance the understanding of low-altitude airbursts by developing the means to model them at extremely high resolution in order to span the scales of entry physics as well as blast wave and plume formation. Small asteroid impacts on Earth are a recognized hazard, but the full nature of the threat is still not well understood. We used shock physics codes to discover emergent phenomena associated with low-altitude airbursts such as the Siberian Tunguska event of 1908 and the Egyptian glass-forming event 29 million years ago. The planetary defense community is beginning to recognize the significant threat from such airbursts. Low-altitude airbursts are the only class of impacts that have a significant probability of occurring within a planning time horizon. There is roughly a 10% chance of a megaton-scale low-altitude airburst event in the next decade.The first part of this LDRD final project report is a preprint of our proceedings paper associated with the plenary presentation at the Hypervelocity Impact Society 2007 Symposium in Williamsburg, Virginia (International Journal of Impact Engineering, in press). The paper summarizes discoveries associated with a series of 2D axially-symmetric CTH simulations. The second part of the report contains slides from an invited presentation at the American Geophysical Union Fall 2007 meeting in San Francisco. The presentation summarizes the results of a series of 3D oblique impact simulations of the 1908 Tunguska explosion. Because of the brevity of this late-start project, the 3D results have not yet been written up for a peer-reviewed publication. We anticipate the opportunity to eventually run simulations that include the actual topography at Tunguska, at which time these results will be published.3

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TYPE SAND Report YEAR 2007
DOIDOIOSTIOSTI
Results 77776–77800 of 96,771
Results 77776–77800 of 96,771