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Preprint
Balanced Viscosity solutions to a rate-independent system for damage
(2017-05-02)
This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems. While in the first two papers [KRZ13, KRZ15] the assumptions on the spatial domain $\Omega$ were kept as general as possible (i.e. nonsmooth domain with mixed boundary conditions), we assume here that $\partial\Omega$ is smooth and that the type of boundary conditions does not change. This smoother setting allows us to derive enhanced regularity spatial properties both for the ...
Preprint
Numerical Methods for Non-Stationary Stokes Flow
(2008)
We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, ...
Konferenzveröffentlichung
Propagation and branching strategies for job shop scheduling minimizing the weighted energy consumption
(2023)
We consider a job shop scheduling problem with time windows, flexible energy prices, and machines whose energy consumption depends on their operational state (offline, ramp-up, setup, processing, standby or ramp-down). The goal is to find a valid schedule that minimizes the overall energy cost. To solve this problem to optimality, we developed a branch-and-bound algorithm based on a time-indexed integer linear programming (ILP) formulation, which uses binary variables that describe blocks spanning multiple inactive ...
Konferenzveröffentlichung
Identifying critical demand periods in capacity planning for networks including storage
(2023)
We consider a capacity planning problem for networks including storage. Given a graph and a time series of demands and supplies, we seek for integer link and storage capacities that permit a single commodity flow with valid storage in- and outtakes over all time steps. This problem arises, for example, in power systems planning, where storage can be used to buffer peaks of varying supplies and demands. For typical time series spanning a full year at hourly resolution, this leads to huge optimization models. To reduce ...