hypersphere_2014_siam_seas

hypersphere_2014_siam_seas, "A Hyperspherical Method for Discontinuity Location in Uncertainty Quantification", given at the SIAM SEAS conference, held at the Florida Institute of Technology, Melbourne, Florida, 28-30 March 2014, representing joint work with Clayton Webster and Guannan Zhang of Oak Ridge National Laboratory.

You may refer to an abstract in hypersphere_2014_siam_seas.txt

• hypersphere_2014_siam_seas.tex
• hypersphere_2014_siam_seas.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).