uq_2012_siam

uq_2012_siam, "Collocation for Uncertainty Quantification", a talk at the SIAM conference on Uncertainty Quantification, held in Raleigh, North Carolina from 2 April 2012 to 06 April 2012.

The talk was part III of a tutorial called "Analysis of SPDE's and Numerical Methods for UQ", prepared and presented mainly by Clayton Webster.

• uq_2012_siam.tex
• uq_2012_siam.pdf

The following files were used:

• adaptive.png, 5 images suggesting the development of an adaptive grid.
• aniso_grids.png, the abscissas of a sequence of 5 anisotropic grids.
• aniso_nine.png, 9 images showing the developement of a sequence of anisotropic grids.
• casl_logo.png, a logo for CASL.
• cc_d3_level2.png, the abscissas of the level 2, dimension 3 Clenshaw Curtis sparse grid.
• cc_grid_sequence.png, displays 2D Clenshaw-Curtis sparse grids of levels 0, 1, 2, 3, 4 and 5.
• cc_level2_closeup.png, the precision of the level 2, dimension 2 Clenshaw Curtis sparse grid.
• cc_level3_closeup.png, the precision of the level 3, dimension 2 Clenshaw Curtis sparse grid.
• cc_level4_closeup.png, the precision of the level 4, dimension 2 Clenshaw Curtis sparse grid.
• cc_sequence.png, displays the nesting behavior of the chosen set of Clenshaw Curtis rules.
• ccs_level4_closeup.png, the precision of the level 4, dimension 2 "slow" Clenshaw Curtis sparse grid.
• d10_con.png, integration test with Genz "Continous" function for dimension 10.
• d10_cpeak.png, integration test with Genz "Corner Peak" function for dimension 10.
• d10_discon.png, integration test with Genz "Discontinous" function for dimension 10.
• d10_gauss.png, integration test with Genz "Gaussian" function for dimension 10.
• d10_oscill.png, integration test with Genz "Oscillatory" function for dimension 10.
• d10_ppeak.png, integration test with Genz "Product Peak" function for dimension 10.
• d6_ppeak.png, integration test with Genz "Product Peak" function for dimension 6.
• diffusion_mc.png, error plots for the diffusion equation, Monte Carlo estimates.
• diffusion_mc_and_sg.png, error plots for the diffusion equation, Monte Carlo and sparse grid estimates.
• fsu_logo.pdf, a logo for FSU.
• ghxcc_level4.png, a plot of a 2D sparse grid formed from Gauss Hermite rules in X and Clenshaw Curtis rules in Y.
• grid_04.png, the abscissas of the sparse grid A(2,2).
• increasing_dimension_cc.png, the (increasing) quadrature error for a Clenshaw Curtis sparse grid in dimensions 3, 4, 5, 6, 7, and 8.
• interp.m, a MATLAB program for computing constant, linear and quadratic interpolants to data, and computing the quadrature error made by integrating each.
• interp_six.png, six plots displaying constant, linear and quadratic interpolants, and the quadrature error encountered when integrating each.
• mydef.sty, a style file with some definitions.
• ncc_5x5x5.png, the abscissas for a 5x5x5 Newton-Cotes rule.
• newdoe.png, a banner for the Department of Energy.
• ornl_header.png, a banner for Oak Ridge National Laboratory.
• ppeak_plot.png, a plot of a 2D version of the Genz product peak test function.
• product_grids2.png, the product grids used to construct a sparse grid.
• quadrature_error_cc.png, the quadrature error made by various sampling approaches, now including the Clenshaw Curtis product rule.
• quadrature_error_sample.png, the quadrature error made by various sampling approaches.
• rgb_tex, definitions of colors.
• sample_points.png, six plots suggesting ways of sampling the unit square.
• siam_logo.pdf, a logo for SIAM.
• utbornl.png, a logo for UT-Battelle.