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We analyse and further develop a hierarchical multiscale method for the numerical simulation of two-phase flow in highly heterogeneous porous media. The method is based upon a mixed finite-element formulation, where fine-scale features are incorporated into a set of coarse-grid basis functions for the flow velocities. By using the multiscale basis… (More)

The algebraic structure underlying non-commutative Lie-Butcher series is the free Lie algebra over ordered trees. In this paper we present a characterization of this algebra in terms of balanced Lyndon words over a binary alphabet. This yields a systematic manner of enumerating terms in non-commutative Lie-Butcher series. 1 Summary Let g be the free Lie… (More)

Motivated by recent developments in numerical Lie group integrators, we introduce a family of local coordinates on Lie groups denoted generalized polar coordinates. Fast algorithms are derived for the computation of the coordinate maps, their tangent maps and the inverse tangent maps. In particular we discuss algorithms for all the classical matrix Lie… (More)

— In the secondary phase of oil recovery, water flooding is the most common way to sweep remaining oil in the reservoirs. The process can be regarded as a nonlinear optimization problem. This paper focuses on how to handle state constraints in an adjoint optimization framework for such systems. The state constraints are cast as nonlinear inequality… (More)

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