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The topic of the present paper has been motivated by a recent computational approach to identify chemical conformations and conformational changes within molecular systems. After proper discretization, the conformations show up as almost invariant aggregates in reversible nearly uncoupled Markov chains. Most of the former work on this subject treated the(More)
The paper presents the mathematical concepts underlying the new adaptive finite element code KASKADE, which, in its present form, applies to linear scalar second-order 2-D elliptic problems on general domains. Starting point for the new development is the recent work on hierarchical finite element bases due to Yserentant (1986). It is shown that this(More)
The focus of this paper is on the eecient solution of boundary value problems involving the double{curl operator. Those arise in the computation of electromagnetic elds in various settings, for instance when solving the electric or magnetic wave equation with implicit timestepping, when tackling time{harmonic problems or in the context of eddy{current(More)
In cranio-maxillofacial surgery physicians are often faced with the reconstruction of massively destroyed or radically resected tissue structures caused by trauma or tumours. Also corrections of dislocated bone fragments up to the complete modeling of facial regions in cases of complex congenital malformations are common tasks of plastic and reconstructive(More)
A family of secant methods based on general rank-1 updates has been revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broy-den's "good" and "bad" update techniques play a special role — but should be associated with two different line search principles. For Broyden's "bad" update(More)
Despite the fact that more than 100 million women worldwide use birth control pills and that half of the world's population is concerned, the menstrual cycle has so far received comparatively little attention in the field of mathematical modeling. The term menstrual cycle comprises the processes of the control system in the female body that, under healthy(More)
In systems biology, the stochastic description of biochemical reaction kinetics is increasingly being employed to model gene regulatory networks and signalling pathways. Mathematically speaking, such models require the numerical solution of the underlying evolution equation, known as the chemical master equation (CME). Up to now, the CME has primarily been(More)
The paper presents basic concepts of a new type of algorithm for the numerical computation of what the authors call the essential dynamics of molecular systems. Mathematically speaking, such systems are described by Hamiltonian diierential equations. In the bulk of applications, individual trajectories are of no speciic interest. Rather, time averages of(More)