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A multiscale discontinuous Galerkin method with the computational structure of a continuous Galerkin method

Computer Methods in Applied Mechanics and Engineering

Hughes, Thomas J.R.; Scovazzi, Guglielmo S.; Bochev, Pavel B.; Buffa, Annalisa

Proliferation of degrees-of-freedom has plagued discontinuous Galerkin methodology from its inception over 30 years ago. This paper develops a new computational formulation that combines the advantages of discontinuous Galerkin methods with the data structure of their continuous Galerkin counterparts. The new method uses local, element-wise problems to project a continuous finite element space into a given discontinuous space, and then applies a discontinuous Galerkin formulation. The projection leads to parameterization of the discontinuous degrees-of-freedom by their continuous counterparts and has a variational multiscale interpretation. This significantly reduces the computational burden and, at the same time, little or no degradation of the solution occurs. In fact, the new method produces improved solutions compared with the traditional discontinuous Galerkin method in some situations. © 2005 Elsevier B.V. All rights reserved.

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TYPE Journal Article YEAR 2006
ScopusOSTI

Verification of LHS distributions

Swiler, Laura P.

This document provides verification test results for normal, lognormal, and uniform distributions that are used in Sandia's Latin Hypercube Sampling (LHS) software. The purpose of this testing is to verify that the sample values being generated in LHS are distributed according to the desired distribution types. The testing of distribution correctness is done by examining summary statistics, graphical comparisons using quantile-quantile plots, and format statistical tests such as the Chisquare test, the Kolmogorov-Smirnov test, and the Anderson-Darling test. The overall results from the testing indicate that the generation of normal, lognormal, and uniform distributions in LHS is acceptable.

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TYPE SAND Report YEAR 2006
DOIOSTI

Multilinear operators for higher-order decompositions

Kolda, Tamara G.; Dunlavy, Daniel D.; Kegelmeyer, William P.

We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The first operator, which we call the Tucker operator, is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor and can be employed to concisely express the Tucker decomposition. The second operator, which we call the Kruskal operator, is shorthand for the sum of the outer-products of the columns of N matrices and allows a divorce from a matricized representation and a very concise expression of the PARAFAC decomposition. We explore the properties of the Tucker and Kruskal operators independently of the related decompositions. Additionally, we provide a review of the matrix and tensor operations that are frequently used in the context of tensor decompositions.

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TYPE SAND Report YEAR 2006
DOIOSTI
Results 9301–9325 of 9,998
Results 9301–9325 of 9,998