Model-reduced inverse modeling

Abstract

Although faster computers have been developed in recent years, they tend to be used to solve even more detailed problems. In many cases this will yield enormous models that can not be solved within acceptable time constraints. Therefore, there is a need for alternative methods that simulate such models more efficiently ans conserve the detailed information. Within this frame, this thesis presents two methodologies. The first method reduces the problem locally by increasing the computation scale (upscaling). Though this method is rather straigthforward, the accuracy is always less than the original model simply because the information on a lower scale needs to be grouped together for a computation at a higher scale. This can be best grouped together by using the original solution. The second method reduces the problem globally by reducing its state space with respect to its behavior (model reduction). Roughly speaking, it breaks up a specific behavior into different components from which the original behavior can be resolved again. The method is promising for scenario analysis and appears to be an improved alternative for inverse modeling.