A Posteriori Error Analysis and Uncertainty Quantification for Adaptive Multiscale Operator Decomposition Methods for Multiphysics Problems

This project was concerned with numerical solution and quantification of accuracy of numerical solution of multiphysics systems that couple together different physical processes acting across a long range of scales are encountered in virtually all areas of interest to Defense Threat Reduction Agency. The overall goal of this project was to develop a mathematically sound yet computationally practical methodology for estimating and mitigating the effects of error and uncertainty in information computed from numerical solutions of multiphysics problems. In addition, the proposed work provided computational tools for modern prediction, uncertainty quantification, parameter optimization, and verification and validation. A primary goal of this project was to construct a posteriori analysis framework for a number of multiphysics problems important to the DTRA mission. They used the results to devise innovative adaptive discretization algorithms. They also used the methods to develop and analyze fast methods for forward and inverse sensitivity analysis of multiphysics problems.