Porous flow as a high dimensional challenge

Monday, October 18, 2010 - 9:30am - 10:30am
Keller 3-180
Ian Sloan (University of New South Wales)
The problem of flow through a porous medium, with the
permeability treated as a Gaussian
random field, can be thought of as a high-dimensional problem:
the dimensionality might be
the number of terms in a truncated Karhunen-Loève expansion;
or (as we prefer) the number
of points in a discrete sampling of the porous medium. In this
paper, describing recent joint
work with F Kuo, I Graham, D. Nuyens and R Scheichl, we explore
the use of quasi-Monte
Carlo methods to study various expected values of the flow
through the medium, and to
compare the results with the Monte Carlo method. The problem is
computationally difficult
if the permeability changes markedly from point to point, but
the numerical results (obtained
by evaluating integrals with as many as one million dimensions)
are encouraging.
MSC Code: