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.
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).
Last revised on 12 February 2024.