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Project
This paper proposes a new mathematical model for the open pit mine planning problem,
based on continuous functional analysis. The traditional models for this problem have been
constructed by using discrete 0-1 decision variables, giving rise to large-scale combinatorial
and Mixed Integer Programming (MIP) problems. Instead, we use a continuous approach
which allows for a refined imposition of slope constraints associated with geotechnical stability.
The model introduced here is posed in a suitable functional space, essentially the
real-valued functions that are Lipschitz continuous on a given two dimensional bounded region.
We derive existence results and investigate some qualitative properties of the solutions
A duality based semismooth Newton framework for solving variational inequalities of the second kind
(2010)
In an appropriate function space setting, semismooth Newton methods are proposed
for iteratively computing the solution of a rather general class of variational inequalities (VIs) of the
second kind. The Newton scheme is based on the Fenchel dual of the original VI problem which
is regularized if necessary. In the latter case, consistency of the regularization with respect to the
original problem is studied. The application of the general framework to specific model problems
including Bingham flows, simplified friction, or total variation regularization in mathematical imaging
is described in detail. Finally, numerical experiments are presented in order to verify the theoretical
results.
We propose a generalization of the Structured Doubling Algorithm (SDA) to compute invariant subspaces
of structured matrix pencils
that arise in the context of solving linear quadratic optimal control problems.
The new algorithm is
designed to attain better accuracy when the classical Riccati equation approach for the solution of the optimal control problem is not well suited because
the stable and unstable invariant subspaces are not well separated (due to eigenvalues near or on the imaginary
axis) or in the case when the Riccati solution does not exist at all. We analyze the convergence
of the method and compare the new method with the classical SDA algorithm as well as some recent structured QR-methods.
Bovine fertility is the subject of extensive research in animal sciences,
especially because fertility of dairy cows has declined during the last
decades. The regulation of estrus is controlled by the complex interplay
of various organs and hormones. Mathematical modeling of the bovine
estrous cycle could help in understanding the dynamics of this complex
biological system. In this paper we present a mechanistic mathematical
model of the bovine estrous cycle that includes the processes of follicle
and corpus luteum development and the key hormones that interact to
control these processes. The model generates successive estrous cycles of
21 days, with three waves of follicle growth per cycle. The model contains
12 differential equations and 54 parameters. Focus in this paper is on
development of the model, but also some simulation results are presented,
showing that a set of equations and parameters is obtained that describes
the system consistent with empirical knowledge. Even though the majority
of the mechanisms that are included in the model are based on relations
that in literature have only been described qualitatively (i.e. stimulation
and inhibition), the output of the model is surprisingly well in line with
empirical data. This model of the bovine estrous cycle could be used
as a basis for more elaborate models with the ability to study effects of
external manipulations and genetic differences.
We propose a robust and efficient numerical discretization scheme for the infinitesimal generator of a diffusion process based on a finite volume approximation. The resulting discrete-space operator can be interpreted as a jump process on the mesh whose invariant measure is precisely the cell approximation of the Boltzmann distribution of the original process. Moreover the resulting jump process preserves the detailed balance property of the original stochastic process.
The aim of this paper is to devise an adaptive timestep control in the contact--stabilized Newmark method (CONTACX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini's condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact--stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.
This paper presents three different adaptive algorithms for eigenvalue problems
associated with non-selfadjoint partial differential
operators. The basis for the developed algorithms is a homotopy method.
The homotopy method starts from a well-understood selfadjoint problem,
for which well-established adaptive methods are available.
Apart from the adaptive grid refinement, the progress of the homotopy as
well as the solution of the iterative method are adapted to balance the contributions
of the different error sources.
The first algorithm balances the homotopy, discretization and approximation errors with respect
to a fixed step-size $\tau$ in the homotopy.
The second algorithm combines the adaptive step-size control for the homotopy
with an adaptation in space that ensures an error below a fixed tolerance $\varepsilon$.
The third algorithm allows the complete adaptivity in space,
homotopy step-size as well as the iterative algebraic eigenvalue solver.
All three algorithms are compared in numerical examples.
We introduce an electronic model for solar cells including energy resolved defect
densities. The resulting drift-diffusion model corresponds to a generalized
van Roosbroeck system with additional source terms coupled with ODEs containing space and
energy as parameters for all defect densities. The system has to be considered in
heterostructures and with mixed boundary conditions from device simulation.
We give a weak formulation of the problem. If the boundary data and the sources
are compatible with thermodynamic equilibrium the free energy along solutions
decays monotonously. In other cases it may be increasing, but we estimate its growth.
We establish boundedness and uniqueness results and prove the existence of a
weak solution. This is done by considering a regularized problem, showing its
solvability and the boundedness of its solutions independent of the regularization level.