Order reduction of large scale DAE models

A technique for the adaptive order reduction of large scale non-linear differential algebraic equations (DAEs) is outlined in this report. The order reduction is adaptive, requiring no preprocessing simulations or special model configuration. The required tuning parameters are the error tolerances for the DAE variables. The order reduction is accomplished in three steps. First, adaptive proper orthogonal decomposition (POD) is used to reduce the number of differential states. POD is made adaptive by dynamically adjusting the order of the reduced model based on the magnitude of the ordinary differential equation (ODE) residuals. As a second step, the algebraic states are partitioned into successive implicit sets of variables and equations by reconstructing the sparsity pattern into a lower triangular block form. Finally, in situ adaptive tabulation (ISAT) is used to adaptively transform the implicit sets into linear explicit approximations. Special consideration of large scale models permits non-linear model reduction theory to be extended to an open equation format.