Title: Accuracy, Precision and Efficiency with Sparse Grids 

Speaker: John Burkardt, Ph.D, Virginia Tech, Advanced Research Computing

Date/Time: Thursday, July 23, 2009, 10:00 – 11:00am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: In the quest for accuracy, modern computational science has been driven into abstract spaces of very high dimension.  These spaces can represent the problem very well, but extracting a numerical answer requires the formidable  task of approximating an integral in a high dimensional space. The Monte Carlo method is always useful for these kinds  of approximations, no matter what the integrand function. The robustness of this method comes at a cost of a limited convergence rate. Especially when a problem comes from a probabilistic or stochastic setting, the integrand function is likely to be very smooth. In this case, sparse grid rules can be formulated which are competitive with the Monte Carlo approach.  We will introduce sparse grids by definition, construction, pictures, and application.  We will then explore how the precision of a sparse grid, achieved efficiently, results in an accurate integral estimate at a reasonable cost.

CSRI POC: Michael Eldred, (505) 844-6479