The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit has been developed at Sandia National Laboratories and provides a flexible, extensible interface between engineering analysis codes for performing uncertainty quantification and parameter sensitivity studies as well as other functionality. We have been utilizing this DoE toolkit in studies of the reduction of discretization and sampling error in evaluation of statistical information about output distributions obtained from finite element studies.

For uncertainty quantification (UQ) work, Dakota provides sophisticated sampling strategies such as Latin Hypercube for investigating an entire probability distribution of potentially correlated input parameters, with “smart” sampling strategies such as bootstrap sampling, importance sampling, quasi-Monte Carlo, and Markov Chain Monte Carlo in development. Dakota provides pseudorandom input samples to and analyzes the output responses of third party simulation tools, computing statistical information about the probability distributions of those response functions. For more expensive engineering simulations where rigorously sampling an entire parameter space is prohibitive, Dakota provides quasi-analytic UQ strategies such as advanced-mean-value methods and reliability methods for determining most probable points of failure.

As part of collaborative studies with colleagues at Sandia, Dakota has been ported to newer Linux distributions, installed in the CFDLab at UT, and interfaced with the open source software library libMesh discussed in the previous section. Using this library coupled together with two libMesh application ‘modules” we have made several exploratory uncertainty quantification studies. Results of one of these studies were provided to Dr. R. J. MacKinnon at Sandia as part of this collaboration and were presented by Dr. Carey at a DoD workshop at ERDC. Part of this study was to examine the selection of mesh parameter h characterizing the finite element discretization and selecting the sample size of the Monte Carlo simulation in Dakota. By using finite element error estimates and Monte Carlo error bounds at a specified confidence interval, estimates of the total work required and total error incurred in a Monte Carlo Finite Element Method were generated, which allows a choice of mesh size and sample size optimized to meet a specified error tolerance while minimizing the computational work required for a specific problem. This initial work was carried out for outcome analysis due to uncertainty in a material coefficient. The ongoing work is carrying this forward into studies exploiting the AMR capability in Libmesh for multiresolution analysis and for coupled multiphysics simulation. Both topics are central to the proposed work. A paper documenting these preliminary studies and their extensions is in preparation.