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Nonoverlapping domain decomposition for optimal control problems governed by semilinear models for gas ﬂow in networks

Leugering G., Martin A., Schmidt M., Sirvent M.

Control and Cybernetics

2017

Vol. 46, no. 3

191--225

We consider optimal control problems for gas ﬂow in pipeline networks. The equations of motion are taken to be represented by a ﬁrst-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a nonoverlapping domain decomposition of the optimal control problem on the graph into local problems on smaller sub-graphs—ultimately on single edges. We prove convergence of the domain decomposition method on networks and study the wellposedness of the corresponding time-discrete optimal control problems. The point of the paper is that we establish virtual control problems on the decomposed subgraphs such that the corresponding optimality systems are in fact equal to the systems obtained via the domain decomposition of the entire optimality system.

Probabilistic methods for estimating the long-term spatial characteristics of monogenetic volcanoes in Japan

Martin A., Takahashi M., Umeda K., Yusa Y.

Acta Geophysica Polonica

2003

Vol. 51, nr 3

271-289

The long-term future spatial distribution of monogenetic volcanoes is much more difficult to estimate than for polygenetic volcanoes because the location of the next eruption forming a new edifice is different. Current knowledge of the complex geological factors and natural processes controlling the locations of monogenetic volcanoes is insufficient to estimate future spatial and temporal patterns. This has been achieved instead through the development and application of the probabilistic and statistical approach, especially during the last two decades. In Japan, a lot research has been focused on the construction of volcanic hazard maps in the event of a volcanic eruption for natural disaster management - the consequences of volcanism - but not the probability of new volcanic edifices forming within or nearby volcanic fields for geological disposal. In this paper, the development of the probabilistic approach is described and the results of probabilistic case studies on the Higashi-Izu (59 vents) and the Kannabe -Oginosen (38 vents) Monogenetic Volcano Groups In Japan are reported using: (1) a spatial model; and (2) a spatio-temporal nearest-neighbor model. The accuracy of each model is also examined.