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
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 07 February 2024.