An application of the discrete maximum principle to designing ultradeep drills — The casing optimization

Because of the increasing importance of ultradeep drills in oil exploring, the casing optimization is of increasing relevance. First, the structure of the problem will be discussed. Second, a model based on the directional convex maximum principle will be introduced. Then we discuss an (exact) method which generates minimal material costs and, finally, we compute the numerical solution by taking a simple example. Compared with models which are based on dynamic programming our model will have substantially fewer numerical requirements.