A Computational Infrastructure for Reliable Computer Simulations

The reliability of computer simulations of physical events or of engineering systems has emerged as the single most critical issue facing advancements in computational engineering and science. Without concrete and quantifiable measures of reliability, the confidence and usefulness of computer predictions are severely limited and the value of computer simulation, in general, is greatly diminished. This paper describes a mathematical and computational infrastructure for the systematic validation of computer simulations of complex physical systems and presents procedures for the integration of computer-based verification and validation processes into simulations. A general class of applications characterized by variational boundary-value problems in continuum mechanics is considered, but the approach is valid for virtually all types of models used in simulations. To simulate a particular feature or attribute of a physical event, four basic concepts are used: 1) hierarchical modeling and a posteriori estimation of modeling error, 2) a posteriori error estimation of approximation error, 3) quantification of uncertainty in the data and in the predicted response, and 4) the development of dynamic a data management paradigm, based on code composition of associated code interfaces and use of annotated source code. The result is a computational framework for computing bounds on, and estimating accuracy of, computer predictions of user-specified features of the response of physical systems.