# Schedule for: 16w5030 - Fifth Parallel-in-time Integration Workshop

Beginning on Sunday, November 27 and ending Friday December 2, 2016

All times in Banff, Alberta time, MST (UTC-7).

Sunday, November 27 | |
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16:00 - 17:30 | Check-in begins at 16:00 on Sunday and is open 24 hours (Front Desk - Professional Development Centre) |

17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |

20:00 - 22:00 | Informal gathering (Corbett Hall Lounge (CH 2110)) |

Monday, November 28 | |
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07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |

08:45 - 09:00 | Introduction and Welcome by BIRS Station Manager (TCPL 201) |

09:00 - 09:30 | Matthew Emmett: Welcome (TCPL 201) |

09:30 - 10:00 |
Martin Gander: Space-Time Parallel Methods Based on Domain Decomposition ↓ Domain decomposition methods like the classical Schwarz method and the
Dirichlet-Neumann and Neumann-Neumann methods have historically been
developed for steady partial differential equations. All these methods
have however also a natural waveform relaxation extension to time
dependent partial differential equations. These waveform relaxation
variants are still based on a spatial decomposition of the physical
domain into subdomains, but then time dependent problems are solved in
the subdomains, and information is exchanged on the space-time
interfaces between subdomains in an iteration that converges in
space-time to the underlying solution of the evolution problem. While
domain decomposition methods for steady problems converge linearly,
the waveform relaxation variants exhibit superlinear convergence for
parabolic problems, and often become direct solvers for hyperbolic
problems. After a simple introduction to the main classes of domain
decompositions for steady problems, I will give in my talk an overview
over the development of their waveform relaxation variants as it
happened over the past 20 years. (TCPL 201) |

10:00 - 10:30 | Coffee Break (TCPL Foyer) |

10:30 - 11:00 |
Daniel Ruprecht: Parareal's discrete dispersion relation ↓ While it has been established that Parareal has stability problems for
hyperbolic and advection-dominated problems, details of how it
propagates waves are less well understood. The talk will show how,
starting from the interpretation of Parareal as a preconditioned fixed
point iteration, one can derive a stability function for linear
problems. After ``normalising'' this function to a unit time interval
it is then possible to derive and analyse a discrete dispersion
relation for Parareal. This allows to estimate the impact of e.g. the
choice of propagators, size of fine and coarse time step, number of
time slices etc. on Parareal's wave propagation characteristics. In
particular, I will discuss the effects of phase and amplitude errors
in the coarse method on convergence. The formulation also allows a
worst case estimate for convergence through the maximum singular value
of the error propagation matrix. This allows to link the number of
iterations to the number of processors in the speedup model and to
make better predictions about weak scaling of Parareal. (TCPL 201) |

11:00 - 11:30 |
Dieter Moser: A multigrid perspective on PFASST ↓ For time-dependent PDEs, parallel-in-time integration using the
"parallel full approximation scheme in space and time" (PFASST) is a
promising way to accelerate existing space-parallel approaches beyond
their scaling limits. While many use cases and benchmarks exist, a
solid and reliable mathematical foundation is still missing. In this
talk, we formulate PFASST as a specialized FAS multigrid method. We
use spectral deferred corrections for the definition of block
smoothers and define the appropriate coarse grid correction to
establish a tight link between PFASST and standard multigrid methods,
providing an easy access to the mathematical analysis and algorithmic
optimization. Using local Fourier analysis, we describe first steps
towards a semi-algebraic convergence analysis for the linear case and
show some results for diffusive and advective prototype problems. (TCPL 201) |

11:30 - 13:00 | Lunch (Vistas Dining Room) |

13:00 - 14:00 |
Guided Tour of The Banff Centre ↓ Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus. (Corbett Hall Lounge (CH 2110)) |

14:00 - 14:20 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. Please don't be late, or you will not be in the official group photo! The photograph will be taken outdoors so a jacket might be required. (TCPL Foyer) |

14:30 - 15:00 |
Jacob Schroder: Two-level convergence theory for multigrid reduction in time (MGRIT) ↓ The need for parallel-in-time is being driven by changes in computer
architectures, where future speedups will be available through greater
concurrency, but not faster clock speeds, which are stagnant. This
leads to a bottleneck for sequential time marching schemes, because
they lack parallelism in the time dimension. In this talk, we examine
an optimal-scaling parallel time integration method, multigrid
reduction in time (MGRIT). MGRIT applies multigrid reduction to the
time dimension by solving the (non)linear systems that arise when
solving for multiple time steps simultaneously. The result is a
versatile approach that is nonintrusive and wraps existing time
evolution codes. In this talk, we present the MGRIT framework and then
discuss some recent theoretical convergence results. Some typical
simplifying assumptions are made, such as a two-grid method, uniform
time-line and constant coefficient PDE. The convergence estimates are
then explored in a variety of settings, including common parabolic and
hyperbolic spatial discretizations coupled with implicit Runge-Kutta
time-stepping schemes. Overall, the convergence estimates are sharp
when compared to numerical experiments and are good predictors of
multilevel results. LLNL-ABS-695327 (TCPL 201) |

15:00 - 15:30 | Coffee Break (TCPL Foyer) |

15:30 - 17:30 |
Benjamin Ong: RIDC Workshop ↓ RIDC software workshop (TCPL 201) |

17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |

Tuesday, November 29 | |
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07:00 - 08:30 | Breakfast (Vistas Dining Room) |

08:30 - 09:00 |
Ruth Schöbel: PFASST and Finite Elements ↓ The "parallel full approximation scheme in space and time" (PFASST) is an iterative, multilevel
strategy for the temporal parallelization of ODEs and discretized PDEs. In numerous studies, this
approach has been successfully coupled to space-parallel solvers which use finite differences,
spectral methods or even particles for discretization in space. In this talk, we will report on our
experience using PFASST in time together with finite elements in space. In particular, we discuss
modifications necessary to treat the mass matrix appropriately on all levels of the space hierarchy
and describe a procedure to switch between these levels. For our experiments, the base
implementation is the PFASST++ software, a C++ implementation of PFASST and its building
blocks MLSDC and SDC. In the context of the finite element discretizations we make use of the
"Distributed and Unified Numerics Environment" (DUNE), which is a modular framework for
solving PDEs with grid-based methods. Using this coupling of PFASST++ and DUNE, we will
show first results for a nonlinear two-component Gray-Scott model. This work is conducted within
the project "ParaPhase", where the final goal is the development of a highly scalable space-time
parallel adaptive algorithm for the simulation of phase-field models. (TCPL 201) |

09:00 - 09:30 |
Martin Schreiber: PinTing oscillatory problems with a massively parallel rational approximation ↓ The stagnated increase in CPU frequency and the resulting trend in HPC
towards massively parallel systems poses new challenges for HPC
applications. The ongoing trend towards massive parallelism
(accelerator cards and many-core systems) requires redesigning
existing algorithms to cope with these architectures. In this
presentation we will focus on oscillatory problems. Solving them with
a regular time stepping method leads to a timestep-by-step
sequentialization in the time dimension. In combination with the CFL
limitation, an increasing resolutions also results in an increase in
the number of these sequential time steps. For problems which are
already limited in their scalability this directly leads to an
increase in wall clock time which can make the results less valuable
or even useless. Based on underlying properties of oscillatory
problems we make use of a recently developed method of a "rational
approximation of exponential integrator" (REXI). This method uses
features of linear oscillatory problems which allows a massively
parallel formulation. This yields several beneficial advantages:
e.g. an increase in resolution does not lead to an increase in the
number of time steps as it is the case with conventional time stepping
methods. In contrast, it leads to an increase in the degree of
parallelization. Our results show speedups of over 2 orders of
magnitude compared to a standard time stepping method and a
scalability model indicates robust scalability beyond 100k cores in
case of large time step sizes. Finally, an extension to a
semi-Lagrangian time stepping scheme to cope with non-linearities will
be discussed. (TCPL 201) |

09:30 - 10:00 |
Thibaut Lunet: On the time-parallelization of the solution of Navier-Stokes equations using Parareal ↓ Unsteady turbulent flow simulations using the Navier Stokes equations
require larger and larger problem sizes. On an other side, new
supercomputer architectures will be available in the next decade, with
computational power based on a larger number of cores rather than
significantly increased CPU frequency. Hence most of the current
generation CFD software will face critical efficiency issues if
bounded to massive spatial parallelization and we consider
time parallelization as an attractive alternative to enhance
efficiency on multi- cores architectures. Several algorithms developed
in the last decades (Parareal, PFASST) may be straightforwardly
applied to the Navier-Stokes equations, but the Parareal algorithm
remains one of the simplest solutions in the case of explicit time
stepping, compressible flow Based on an optimized implementation of
Parareal,3 we modelize the speed-up obtained when combining both space
and time parallelizations. This modelization takes into account the
speedup of an actual structured, massively parallel CFD solver and
the cost of time communications, both measured on two different
supercomputers. Some preliminary requirements for a worthy
time-parallel integration will be then derived, in terms of both
Parareal iteration count and size of the time subdomain window.
We then study within this framework, possible enhancements of the
well-known convergence difficulties for Parareal encountered for
advection dominated problems. The proposed approach is based on the
representation of Parareal as an algebraic system of nonlinear equations solved by a preconditioned Newton’s method. The new formulation
targets the reduction of the degree of non-normality of its Jacobian
by slightly modifying the Parareal iteration.
Performance on examples related to canonical linear problems, like the
Dahlquist and the one- dimensional advection equation, is analysed. To
conclude we comment on the extension of this method to nonlinear
problems. (TCPL 201) |

10:00 - 10:30 | Coffee Break (TCPL Foyer) |

10:30 - 11:30 |
Open Question session ↓ Participants are invited to pose open questions and/or topics for
discussion to the rest of the group. Those wishing to present
questions should prepare quick presentations (2-3 slides) for context.
Participants are encouraged to discuss these questions
openly throughout the remainder of the workshop. (TCPL 201) |

11:30 - 13:00 | Lunch (Vistas Dining Room) |

13:00 - 13:30 |
Wayne Enright: Computing Sensitivities or Solving Parameter Estimation Problems in ODEs and DDEs ↓ In recent years we have developed reliable order $p$ methods for the
approximate solution of general systems of IVPs and DDEs. We have used
these methods to implement effective techniques for parameter
estimation and sensitivity analysis for IVPs and DDEs. The two
techniques we have investigated are the "variational approach" and the
"adjoint approach". We will discuss the cost and reliability of each
approach and identify several factors that contribute to the
performance of each. In particular we will discuss why, for each
technique, the underlying numerical IVP or DDE solver must exploit
inherent parallelism if the number of state variables, the number of
parameters, or the number of data points is large. (TCPL 201) |

13:30 - 14:00 |
Beth Wingate: The role of near-resonance in the convergence of parareal ↓ In recent years we have developed reliable order $p$ methods for the
approximate solution of general systems of IVPs and DDEs. We have used
these methods to implement effective techniques for parameter
estimation and sensitivity analysis for IVPs and DDEs. The two
techniques we have investigated are the "variational approach" and the
"adjoint approach". We will discuss the cost and reliability of each
approach and identify several factors that contribute to the
performance of each. In particular we will discuss why, for each
technique, the underlying numerical IVP or DDE solver must exploit
inherent parallelism if the number of state variables, the number of
parameters, or the number of data points is large. (TCPL 201) |

14:00 - 14:30 |
Andreas Kreienbuehl: Parallel in time climate modeling ↓ We discuss an application of PFASST to simulate climate on a
sphere. For the shallow water equations, the High-Order Methods
Modeling Environment (HOMME) with spectral elements is used. Time
parallelism on the other hand is realized by means of LIBPFASST. The
focus is on implementation as well as efficiency. (TCPL 201) |

14:30 - 15:00 |
Andreas Schmitt: An empirical numerical study of the Parareal method applied to the Burgers Equation ↓ Solving industrial sized problems in the field of computational fluid
dynamics is a big challenge. Especially in flows with high Reynolds
numbers (flows with a high ratio between convection and diffusion)
small turbulent structures have to be resolved with a very fine grid
in space and time. These fine grids lead, even with spatial
parallelization, to long computational times, since also a reasonable
amount of physical time has to be simulated. This problem can be
partially circumvented by modelling the turbulent structures as it is
done with statistical turbulence models. These modelling techniques
allow coarser grids and shorter simulation runtimes with the drawback
of a less accurate solution. Nevertheless, these simulations can still
have a runtime in the range of months. For these problems a
parallelization in time in addition to the parallelization in space is
very appealing. The parallelization in time can be used to reduce the
computational load of the typically longer physical time which is to
be simulated. The easiest parallel in time method, the Parareal
method, would be a good starting point for the runtime
reduction. Unfortunately, it was already shown by multiple
publications, that the Parareal method in its original formulation is
not suitable for high Reynolds flows [e.g. Kreienbuehl et al., 2015].
The Parareal method has stability problems which occur with high
Reynolds number flows. These stability problems can be investigated by
applying the Parareal method to the viscous Burgers equation, which is
closely related to the Navier-Stokes equations. Therefore, a parameter
study was done by varying the Reynolds number of the simulated
flow. In addition, it was investigated whether a scale difference of
the structures in the flow have an impact on the convergence. These
structures which model the turbulent scales are induced according to
[Kooij et al., 2015]. Furthermore, the effect of applying different
time stepping schemes was studied. The used schemes were of explicit
Runge-Kutta and IMEX Runge-Kutta nature. Moreover, it will be
presented whether it is possible to reduce the stability problems of
applying the Parareal method to high Reynolds number flows with a
semi-Lagragian formulation of the examined equations.
The work of Andreas Schmitt is supported by the 'Excellence
Initiative' of the German Federal and State Governments and the
Graduate School of Computational Engineering at Technische
Universit\"at Darmstadt. (TCPL 201) |

15:00 - 15:30 | Coffee Break (TCPL Foyer) |

15:30 - 17:30 | Jacob Schroder: XBraid workshop (TCPL 201) |

17:30 - 19:30 | Dinner (Vistas Dining Room) |

Wednesday, November 30 | |
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07:00 - 08:30 | Breakfast (Vistas Dining Room) |

08:30 - 09:00 |
Stefanie Günther: Adjoint Sensitivity Computation for the Parallel Multigrid Reduction in Time Software Library XBraid ↓ In this paper we present an adjoint solver for the multigrid in time software library XBraid. XBraid
provides a non-intrusive approach for simulating unsteady dynamics on multiple processors while parallelizing not only in space but also in the time domain. It applies an iterative multigrid reduction in time
algorithm to existing spatially parallel classical time propagators and computes the unsteady solution parallel in time. However, in many engineering applications not only the primal unsteady flow computation is of
interest but also the ability to compute sensitivities that determine the influence of design changes to some
output quantity. In recent years, adjoint solvers have widely been developed which propagate sensitivity
information backwards through the time domain.
We develop an adjoint solver for XBraid that enhances the primal iterations by an iteration for computing
adjoint sensitivities. In each iteration, the adjoint code runs backwards through the primal XBraid actions
and computes the consistent discrete adjoint sensitivities parallel in time. It is highly non-intrusive as
existing adjoint time propagators can easily be integrated through the adjoint interface.
We validate the adjoint code by applying it to an unsteady partial differential equation that mimics the
behavior of separated flows past bluff bodies. In our 1D model, the near wake is mimicked by a nonlinear
ODE, namely the Lorenz attractor which exhibits self-excited oscillations. The far wake is modeled by an
advection - diffusion equation whose upstream boundary condition is determined by the ODE mimicking
the near wake. We demonstrate the integration of a serial time stepping algorithm, that solves the PDE
forward in time, into the parallel-in-time XBraid framework as well as the development of the corresponding adjoint interface. The resulting sensitivities are in good agreement with those computed from finite
differences. Nevertheless, there is still great potential for optimizing the performance of the adjoint code
using advanced algorithmic differentiation techniques such as reverse accumulation and checkpointing.
Due to the iterative nature of the primal and the adjoint flow computation, the method is very well suited for
simultaneous optimization algorithms like the One-shot method which solve the optimization problem
in the full space. They have proven to be very efficient for optimization with steady-state PDE constraints
while its application to unsteady PDE is still under development. The non-intrusive adjoint XBraid solver
is therefore highly desirable and will extend its application range from pure simulation to optimization. (TCPL 201) |

09:00 - 09:30 |
Felix Kwok: A Parareal Algorithm for Coupled Systems Arising from Optimal Control Problems ↓ When solving optimal control problems over a long time horizon, one
can introduce additional parallelism in time by subdividing the time
horizon into smaller, non-overlapping time intervals and by solving
these subproblems in parallel. If the intermediate state and adjoint
between time intervals are known exactly, this procedure yields the
exact solution. Thus, the problem reduces to solving a nonlinear
system in these intermediate states, which are related via certain
propagation operators. In this talk, we present a parareal approach
for solving this nonlinear system: here, the global problem is
approximated by a simpler one using coarse propagators, while the fine
propagation is performed in parallel over different time
intervals. One then iterates until the intermediate states are
consistent across time intervals. Unlike parareal for initial value
problems, the coarse problem still contains a forward-backward
coupling, but it is much cheaper to solve than the global fine
problem. We analyze the convergence of the new method for a model
linear problem and illustrate its behaviour numerically for nonlinear
problems in which the control enters as an additive source term. (TCPL 201) |

09:30 - 10:00 |
Benjamin Ong: Pipeline Implementation of Waveform Relaxation Methods ↓ Recently several waveform relaxation algorithms have been proposed,
where the standard Dirichlet or Robin coupling conditions are replaced
by transmission conditions that are implemented in stages, for example
the Dirichlet--Neumann coupling conditions. These new transmission
conditions promise better rates of convergence at the expense, as it
turns out, of parallel efficiency. This talk focuses on a practical
implementation of these new waveform relaxation algorithms, as well as
an analysis of the communication cost and efficiency overhead of these
algorithms. (TCPL 201) |

10:00 - 10:30 | Coffee Break (TCPL Foyer) |

10:30 - 11:00 |
Joerg Wensch: Using time-parallel methods for the simulation of multi-domain parabolic equations ↓ We consider parabolic partial differential equations defined on
multiple domains. These domains are coupled at the boundary by Robin
boundary conditions where the region of overlap is time-dependent. The
rate of change of the geometry is much faster than the time scale of
heat conduction. We apply the spectral deferred correction approach
as well as a splitting in slow and fast components to this type of
problem. We use the PFASST concept to obtain a parallel
implementation of these concepts. One basic ingredient of PFASST are
the underlying spectral deferred correction methods. Spectral deferred
correction (SDC) methods start from a provisional solution. Using a
simpler time integrator, this provisional solution will be iteratively
improved. There are several adaptions of SDC for multi-rate
problems. MISDC methods treat every scale independently in the sweeper
and allows to construct high-order multi-rate methods. Typically,
slow processes are treated explicitly and fast processes
implicitly. We adapt the idea of the MISDC methods for the coupled
heat equation and treat the diffusion part implicitly, but the fast
sources in an explicit manner to avoid implicit solves for the
geometry. The method will be analyzed with respect to order and
stability. Finally, we present numerical results. (TCPL 201) |

11:00 - 11:30 |
Martin Neumüller: Parallel Space-Time Methods ↓ In this talk we discuss stable space-time discretization schemes,
which allow the use of standard parallel finite element libraries to
solve the arising space-time linear systems efficiently. Moreover we
will have a look at space-time multigrid methods which also allow
parallelization with respect to space and time. (TCPL 201) |

11:30 - 13:30 | Lunch (Vistas Dining Room) |

13:30 - 17:30 | Free Afternoon (Banff National Park) |

17:30 - 19:30 | Dinner (Vistas Dining Room) |

Thursday, December 1 | |
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07:00 - 09:00 | Breakfast (Vistas Dining Room) |

09:00 - 09:30 |
Mikio Iizuka: Investigation of Convergence Characteristics of the Parareal method for Hyperbolic PDEs using the Reduced Basis Methods ↓ In this study, we introduce the reduced basis methods (RBMs) to
improve a convergence rate of the Parareal method for hyperbolic PDEs.
We extract a small subspace consisting of main modes that compose the
accurate solution from the data calculated by the fine solver during
iterations. Once we got a set of reduced basis, the computational
cost of time marching becomes low because of the small subspace, and
therefore we can use a fine time step width. Then we can perform a
coarse solver with the time step width same as a fine solver. Thus, it
is expected that the convergence can be improved and the computation
cost can be reduced. However, if the subspace cannot be reduced to
small one, the RBMs maybe does not work well, e.g., for the complex
phenomena such as the turbulence flow. We need to know what case the
RBMs work well for, but currently it is not clear. Therefore, we
investigate the convergence characteristics of the Parareal method for
hyperbolic PDEs which have different complexity with the RBMs. In this
presentation, we discuss about the results of convergence of the
Parareal method with the RBMs for the linear advection equation,
viscous Burgers' equation and Navier-Stokes equations. (TCPL 201) |

09:30 - 10:00 |
Robert Falgout: Space-time adaptivity in the XBraid library ↓ Since clock speeds are no longer increasing, time integration is
becoming a sequential bottleneck. The multigrid reduction in time
(MGRIT) algorithm is an approach for exploiting parallelism in the
time dimension that is designed to build on existing codes and time
integration techniques. The XBraid library is an open source
implementation of MGRIT. One important technique used by current
simulation codes is adaptivity in both space and time. In this talk,
we discuss approaches taken in XBraid to support adaptivity by
exploring several application problems that employ a combination of
mesh refinement, mesh motion, and temporal refinement. (TCPL 201) |

10:00 - 10:30 | Coffee Break (TCPL Foyer) |

10:30 - 11:00 |
Michael Minion: An analysis of PFASST on something other than the heat equation ↓ I will percent analytical and numerical results of the PFASST algoritm
applied to something other than the heat equation. (TCPL 201) |

11:00 - 11:30 |
Shaun Lui: Space-time Legendre Spectral Collocation Methods ↓ Spectral methods solve elliptic PDEs numerically with errors bounded
by an exponentially decaying function of the number of modes when the
solution is analytic. For time dependent problems, almost all focus
has been on low-order finite difference schemes for the time
derivative and spectral schemes for spatial derivatives. Spectral
methods which converge spectrally in both space and time have appeared
recently. This paper shows the exponential convergence of the heat
equation for a Legendre spectral collocation method. A condition
number estimate of the method is also given. (TCPL 201) |

11:30 - 13:00 | Lunch (Vistas Dining Room) |

13:00 - 13:30 |
Robert Speck: Attempts to parallelize SDC ↓ Spectral deferred corrections (SDC) are an easy way to construct
higher-order time integration schemes from simple base integrators,
e.g. backward Euler or velocity-Verlet. In addition, their iterative
nature makes them an attractive subject for investigating
parallelization in time. The most prominent example is the "parallel
full approximation scheme in space in time" (PFASST), which couples
SDC and multigrid techniques in a clever yet slightly intricate
way. While PFASST parallelizes the computation of multiple steps in
time, we will focus on the direct, single-step parallelization of SDC
iterations themselves. In this talk, we will explore different
approaches and show their strengths (if any) as well as their (often
severe) limitations. Results of this investigation will turn out to be
rather diverse, so this talk is also meant to challenge the community
to find better and more robust ways for parallelizing SDC across the
method. (TCPL 201) |

13:30 - 14:00 |
Olga Mula: More on Fully Scalable Balanced Parareal Method ↓ The parareal in time algorithm, combines a serial coarse solver used
on the full time simulation with loops of fine solver, implemented in
parallel, over shorter time simulations. This algorithm uses a new
direction for task decomposition and parallelism for time dependent
(partial) differential equation. One way to improve the parallel
efficiency of the parareal in time algorithm, is to degrade the fist
swap of the fine solver and improve its accuracy over the parallel
iterations.
This degradation and improvement over the loops has to be well
balanced in order not to pollute the convergence efficiency of the
method.
This presentation will propose some mathematical approach for
rigorously sustain this approach. (TCPL 201) |

14:00 - 14:30 |
Stephanie Friedhoff: Exploring the use of XBraid to implement various parallel-in-time methods ↓ Since the introduction of the idea of adding parallelism to time
integration in the seminal work of Nievergelt in 1964, various
approaches for parallel-in-time integration have been explored. One of
these approaches is applying multigrid to the time dimension,
resulting in the multigrid-reduction-in-time (MGRIT) algorithm by
Falgout et al. The corresponding open source code XBraid is flexible,
allowing for a variety of time stepping, relaxation, and temporal
coarsening options. It was recently shown in Bolten et al. that the
time-parallel expansion of spectral deferred corrections methods, the
Parallel Full Approximation Scheme in Space and Time (PFASST)
algorithm by Emmett and Minion, can be described as a
multigrid-in-time method under certain assumptions.
In this talk, we discuss approaches for incorporating aspects of
PFASST and multigrid-based parallel-in-time methods into XBraid. (TCPL 201) |

14:30 - 15:00 |
Martin Weiser: Lossy compression of FE coefficients for reducing communication in time-parallel simulations ↓ Communication bandwidth between nodes of parallel machines grows
slower than the nodes' computational performance and increasingly
becomes a bottleneck of PDE solvers. We present lossy compression
techniques based on multilevel prediction in hierarchical grids and
entropy coding as a means to reduce the amount of data to be
communicated between nodes in SDC-based time-parallel
simulations. Compression rate and impact on convergence depending on
the quantization error are investigated both theoretically and at some
numerical examples realized in the finite element code Kaskade 7,
which leads to an adaptive choice of the quantization threshold. (TCPL 201) |

15:00 - 15:30 | Coffee Break (TCPL Foyer) |

15:30 - 17:30 | Matthew Emmett: PFASST workshop (TCPL 201) |

17:30 - 19:30 | Dinner (Vistas Dining Room) |

Friday, December 2 | |
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07:00 - 08:30 | Breakfast (Vistas Dining Room) |

08:30 - 09:00 | Debasmita Samaddar: Exploring options for the coarse solver in the parareal algorithm for non linear problems in fusion plasma (TCPL 201) |

09:00 - 09:30 |
Olaf Steinbach: Space-time finite and boundary element methods ↓ For the model problem of the heat equation we formulate and describe
space-time finite and boundary element methods. Here the
discretization is done with respect to rather general discretizations
of the space-time cylinder and its boundary. This allows the use of
adaptivity both in space and time, but requires the solution of the
global system at once. Hence, preconditioning and parallelization are
mandatory. Numerical results are given, including first results for
the wave equation. (TCPL 201) |

09:30 - 10:00 | Rolf Krause: An Iterative Approach for Time Integration Based on Discontinuous Galerkin Methods (TCPL 201) |

10:00 - 10:30 | Coffee Break (TCPL Foyer) |

10:30 - 11:00 | Closing remarks (TCPL 201) |

11:30 - 12:00 |
Checkout by Noon ↓ 5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon. (Front Desk - Professional Development Centre) |

12:00 - 13:30 | Lunch from 11:30 to 13:30 (Vistas Dining Room) |