A Posteriori Analysis of Adaptive Multiscale Operator Decomposition Methods for Multiphysics Problems

Abstract

This project was concerned with the accurate computational error estimation for numerical solutions of multiphysics, multiscale systems that couple different physical processes acting across a large range of scales relevant to the interests of the DOE. Multiscale, multiphysics models are characterized by intimate interactions between different physics across a wide range of scales. This poses significant computational challenges addressed by the proposal, including: (1) Accurate and efficient computation; (2) Complex stability; and (3) Linking different physics. The research in this project focused on Multiscale Operator Decomposition methods for solving multiphysics problems. The general approach is to decompose a multiphysics problem into components involving simpler physics over a relatively limited range of scales, and then to seek the solution of the entire system through some sort of iterative procedure involving solutions of the individual components. MOD is a very widely used technique for solving multiphysics, multiscale problems; it is heavily used throughout the DOE computational landscape. This project made a major advance in the analysis of the solution of multiscale, multiphysics problems.