322 research outputs found
A New Parareal Algorithm for Time-Periodic Problems with Discontinuous Inputs
The Parareal algorithm, which is related to multiple shooting, was introduced
for solving evolution problems in a time-parallel manner. The algorithm was
then extended to solve time-periodic problems. We are interested here in
time-periodic systems which are forced with quickly-switching discontinuous
inputs. Such situations occur, e.g., in power engineering when electric devices
are excited with a pulse-width-modulated signal. In order to solve those
problems numerically we consider a recently introduced modified Parareal method
with reduced coarse dynamics. Its main idea is to use a low-frequency smooth
input for the coarse problem, which can be obtained, e.g., from Fourier
analysis. Based on this approach, we present and analyze a new Parareal
algorithm for time-periodic problems with highly-oscillatory discontinuous
sources. We illustrate the performance of the method via its application to the
simulation of an induction machine
A micro-macro parareal algorithm: application to singularly perturbed ordinary differential equations
We introduce a micro-macro parareal algorithm for the time-parallel
integration of multiscale-in-time systems. The algorithm first computes a
cheap, but inaccurate, solution using a coarse propagator (simulating an
approximate slow macroscopic model), which is iteratively corrected using a
fine-scale propagator (accurately simulating the full microscopic dynamics).
This correction is done in parallel over many subintervals, thereby reducing
the wall-clock time needed to obtain the solution, compared to the integration
of the full microscopic model. We provide a numerical analysis of the algorithm
for a prototypical example of a micro-macro model, namely singularly perturbed
ordinary differential equations. We show that the computed solution converges
to the full microscopic solution (when the parareal iterations proceed) only if
special care is taken during the coupling of the microscopic and macroscopic
levels of description. The convergence rate depends on the modeling error of
the approximate macroscopic model. We illustrate these results with numerical
experiments
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
We present a parareal in time algorithm for the simulation of neutron
diffusion transient model. The method is made efficient by means of a coarse
solver defined with large time steps and steady control rods model. Using
finite element for the space discretization, our implementation provides a good
scalability of the algorithm. Numerical results show the efficiency of the
parareal method on large light water reactor transient model corresponding to
the Langenbuch-Maurer-Werner (LMW) benchmark [1]
A micro/macro parallel-in-time (parareal) algorithm applied to a climate model with discontinuous non-monotone coefficients and oscillatory forcing
We present the application of a micro/macro parareal algorithm for a 1-D
energy balance climate model with discontinuous and non-monotone coefficients
and forcing terms. The micro/macro parareal method uses a coarse propagator,
based on a (macroscopic) 0-D approximation of the underlying (microscopic) 1-D
model. We compare the performance of the method using different versions of the
macro model, as well as different numerical schemes for the micro propagator,
namely an explicit Euler method with constant stepsize and an adaptive library
routine. We study convergence of the method and the theoretical gain in
computational time in a realization on parallel processors. We show that, in
this example and for all settings, the micro/macro parareal method converges in
fewer iterations than the number of used parareal subintervals, and that a
theoretical gain in performance of up to 10 is possible
A Decentralized Parallelization-in-Time Approach with Parareal
With steadily increasing parallelism for high-performance architectures,
simulations requiring a good strong scalability are prone to be limited in
scalability with standard spatial-decomposition strategies at a certain amount
of parallel processors. This can be a show-stopper if the simulation results
have to be computed with wallclock time restrictions (e.g.\,for weather
forecasts) or as fast as possible (e.g. for urgent computing). Here, the
time-dimension is the only one left for parallelization and we focus on
Parareal as one particular parallelization-in-time method.
We discuss a software approach for making Parareal parallelization
transparent for application developers, hence allowing fast prototyping for
Parareal. Further, we introduce a decentralized Parareal which results in
autonomous simulation instances which only require communicating with the
previous and next simulation instances, hence with strong locality for
communication. This concept is evaluated by a prototypical solver for the
rotational shallow-water equations which we use as a representative black-box
solver
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