1,707 research outputs found
Microscopic/stochastic timesteppers and coarse control: a kinetic Monte Carlo example
Coarse timesteppers provide a bridge between microscopic / stochastic system
descriptions and macroscopic tasks such as coarse stability/bifurcation
computations. Exploiting this computational enabling technology, we present a
framework for designing observers and controllers based on microscopic
simulations, that can be used for their coarse control. The proposed
methodology provides a bridge between traditional numerical analysis and
control theory on the one hand and microscopic simulation on the other
Parallel-In-Time Simulation of Eddy Current Problems Using Parareal
In this contribution the usage of the Parareal method is proposed for the
time-parallel solution of the eddy current problem. The method is adapted to
the particular challenges of the problem that are related to the differential
algebraic character due to non-conducting regions. It is shown how the
necessary modification can be automatically incorporated by using a suitable
time stepping method. The paper closes with a first demonstration of a
simulation of a realistic four-pole induction machine model using Parareal
Implicit Methods for Equation-Free Analysis: Convergence Results and Analysis of Emergent Waves in Microscopic Traffic Models
We introduce a general formulation for an implicit equation-free method in
the setting of slow-fast systems. First, we give a rigorous convergence result
for equation-free analysis showing that the implicitly defined coarse-level
time stepper converges to the true dynamics on the slow manifold within an
error that is exponentially small with respect to the small parameter measuring
time scale separation. Second, we apply this result to the idealized traffic
modeling problem of phantom jams generated by cars with uniform behavior on a
circular road. The traffic jams are waves that travel slowly against the
direction of traffic. Equation-free analysis enables us to investigate the
behavior of the microscopic traffic model on a macroscopic level. The standard
deviation of cars' headways is chosen as the macroscopic measure of the
underlying dynamics such that traveling wave solutions correspond to equilibria
on the macroscopic level in the equation-free setup. The collapse of the
traffic jam to the free flow then corresponds to a saddle-node bifurcation of
this macroscopic equilibrium. We continue this bifurcation in two parameters
using equation-free analysis.Comment: 35 page
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