hypersphere_2013_ajou

hypersphere_2013_ajou, "A Hyperspherical Method for Discontinuity Location in Uncertainty Quantification", representing joint work with Clayton Webster and Guannan Zhang of Oak Ridge National Laboratory, given at Ajou University, Suwon, Korea, on 13 August 2013.

You may refer to the abstract in hypersphere_2013_ajou.txt.

• hypersphere_2013_ajou.tex
• hypersphere_2013_ajou.pdf

The files used for this presentation include

• 1d_adaptive_spgrid.pdf, shows how the 1D adaptive sparse grid procedure is carried out.
• annulus.png, a triangulated annulus.
• apps.pdf, illustrates some applications in which an uncertainty quantification calculation, of the sort described here, might be needed.
• asg.pdf, grids for the transition zones of the circle and sphere, as generated by the adaptive sparse grid approach.
• ball_3d.png, looks at a 3D ball, the mapping by the hypersphere method, and mappings based on the hierarchical adaptive sparse grid method.
• cylinder_3d.png, looks at a 3D cylinder, the mapping by the hypersphere method, and mappings based on the hierarchical adaptive sparse grid method.
• err_asg.png, the error decay for the adaptive sparse grid method, with increasing number of points, for several dimensions.
• error_decay.png, the error decay for the adaptive sparse grid method, the Monte Carlo method, and the hypersphere method.
• event.pdf, illustrates how a function Z(X,Y) can implicitly generate regions where Z is greater than some tolerance; how Monte Carlo can be used to estimate the size of such regions; and examples of the error decay rate for such estimates.
• fish.png, the outline of a closed domain that might be a candidate for the hypersphere algorithm.
• fsu_oak_ridge_logo.pdf, a logo.
• hbasis.png, piecewise linear, quadratic, and cubic hierarchical basis families.
• shepp_logan.png, a 3D surface plot of the Shepp-Logan function.
• spgrid_2d_2.pdf, illustrates how the adaptive 2D sparse grid procedure works.
• surf_test01_2d.png, a sample plot of discontinuous data, showing two regions in red, surrounded by a blue background.
• surf_test01_3d.png, a 3D version of surf_test01_2d, showing that the discontinuous data is simply the sets of coordinates for which a function is above or below a certain tolerance.
• t2d_contour.png, shows how the algorithm refines its estimate of the shape of the transition zone for a 2D T-PDF.
• transform.png, illustrates the ball and cube surfaces in 3D, and their transformation to a function R(Theta1,Theta2).