The technology of solid oxide fuel cells is one of the important topics in modern engineering. One research direction is to design robust and accurate control strategies for this kind of fuel cells based on models spatially discretized into ordinary differential equations. To allow users to employ new models and techniques easily in combination with different verified and traditional tools, we implement the environment VERICELL. It features an intuitive graphic interface for construction of fuel cell models from predefined building blocks. In this paper, we describe modeling and verification possibilities available in VERICELL for the analysis of solid oxide fuel cells.
In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short overview of possibilities to formulate non-smooth problems and point out connections between the traditional non-smooth theory and interval analysis. Moreover, we summarize already existing verified methods for solving initial value problems with non-smooth (in fact, even not absolutely continuous) right-hand sides and propose a way of handling a certain practically relevant subclass of such systems. We implement the approach for the solver VALENCIA-IVP by introducing into it a specialized template for enclosing the first-order derivatives of non-smooth functions. We demonstrate the applicability of our technique using a mechanical system model with friction and hysteresis. We conclude the paper by giving a perspective on future research directions in this area.
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