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Carpet is a mesh refinement driver
for Cactus. Cactus is a
framework for solving time-dependent partial differential
equations on uniform grids, and Carpet is an extension of Cactus
that makes mesh refinement possible. Carpet was originally written
in 2001
by Erik
Schnetter at
the TAT
(Theoretische Astrophysik Tübingen) and later brought into
production use by Erik Schnetter, Scott Hawley, and Ian Hawke at
the AEI (Max-Planck-Institut
für Gravitationsphysik, Albert-Einstein-Institut). Carpet is
currently maintained at
the CCT (Center for
Computation & Technology)
at LSU. These pages describe
Carpet
and its current development.
News
January 14, 2008: Carpet's communication
infrastructure has been improved significantly, making Carpet
scale to at least 4,000 processors, including mesh refinement.
Using "friendly user time"
on Ranger,
the new 60,000
core TeraGrid
supercomputer
at TACC, we measured
the benchmark results below for a numerical relativity kernel
solving the BSSN equations. These benchmarks emply a hybrid
communication scheme
combining MPI
and
OpenMP, using the shared
memory capabilities of Ranger's nodes to reduce the memory
overhead of parallelisation. We are grateful for the help we
received from Ranger's support team.
The graph below shows weak scaling tests for both unigrid and
mesh refinement benchmarks. The problem size per core was
kept fixed, and there were 4 OpenMP threads per MPI process,
with 1 MPI process per socket. The benchmark was also run
with the PUGH driver for comparison for certain core counts.
As the graphs show, this benchmark scales near perfectly for
unigrid, and has only small variations in run time for nine
levels of mesh refinement.
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![Scaling graph for Ranger](scaling-ranger/results-ranger.png)
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October 3, 2007: Carpet's timing infrastructure has been
extended to automatically measure both time spent computing and
time spent in I/O. The performance of large simulations depends
not only on the computational efficiency and communication
latency, but also on the throughput to file servers. These new
statistics give a real-time overview and can point out
performance problems. The statistics are collected in the
existing Carpet::timing variables.
August 30, 2007: So far this year, ten of the
publications from three research groups examining the dynamics
of binary black hole systems are based on simulations performed
with Cactus and Carpet:
Astrophys. J. 661, 430-436 (2007)
(arXiv:gr-qc/0701143)
Phys. Rev. Lett. 99, 041102 (2007)
(arXiv:gr-qc/0701163)
Astrophys. J. 659, L5-L8 (2007)
(arXiv:gr-qc/0701164)
Phys. Rev. Lett. 98, 231102 (2007)
(arXiv:gr-qc/0702133)
Class. Quantum Grav. 24, 3911-3918 (2007)
(arXiv:gr-qc/0701038)
arXiv:0705.3829 [gr-qc]
arXiv:0706.2541 [gr-qc]
arXiv:0707.2559 [gr-qc]
arXiv:0708.3999 [gr-qc]
arXiv:0708.4048 [gr-qc]
These publications mainly examine the spin dynamics and the
gravitational wave recoil in BBH systems. Since not all
research groups use Cactus and Carpet, this represents only part
of the published work on this subject.
August 26, 2007: In experiments with hybrid
communication schemes
combining MPI
and
OpenMP, we found a 20%
speed improvement when using a single node
of Abe
at NCSA, and a
substantial scaling improvement when using 1024 and more CPUs.
(Abe has 8 CPUs per node.) These experiments included cache
optimisations when traversing the 3D arrays. The tests were
performed with a modified version of
the Cactus WaveToy
example application without using I/O or analysis methods.
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![Scaling graph for Abe](hybrid-scaling/results-wavetoy-abe.png)
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August 15, 2007: We are happy to hear that our
proposal ALPACA: Cactus tools for Application Level Profiling
And Correctness Analysis will be funded by
NSF's SDCI
programme for three years.
The ALPACA
project is aiming at developing complex, collaborative
scientific applications, appropriate for highly scalable
hardware architectures, providing fault tolerance, advanced
debugging, and transparency against new developments in
communication, programming, and execution models. Such tools
are especially rare at the application level, where they are
most critically needed.
July 31, 2007: We are happy to hear that our
proposal XiRel: Cyberinfrastructure for Numerical
Relativity will be funded by
NSF's PIF
programme for three
years. XiRel is
collaborative proposal
by LSU, PSU,
and UTB
(now RIT). The central goal
of XiRel is the development of a highly scalable, efficient, and
accurate adaptive mesh refinement layer based on the current
Carpet driver, which will be fully integrated and supported in
Cactus and optimised for numerical relativity.
February 26, 2007: The thorn LSUPETSc
implements a generic elliptic solver for Carpet's multi-patch
infrastructure, based
on PETSc.
It assumes touching (not overlapping) patches, and uses
inter-patch interface conditions very similar to those developed
by Harald
Pfeiffer. LSUPETSc can solve "arbitrary" systems
of coupled, non-linear elliptic equations. It does not support
mesh refinement.
January 12, 2007: In order to be able to restructure
some of Carpet's internals without disturbing ongoing production
simulations, we have created an experimental version.
The main goals of this experimental version are to improve its
performance on many (>100) processors and to re-arrange some
internal details to simplify future development. Few new
features are planned, but some of the changes may be
incompatible.
Old News...
Documentation
We have accumulated a few pieces of documentation:
- An introduction
(PDF, 210 kB) to Carpet, as well as a guide to the
first steps for using it. Everybody should have read this.
(This is the same as the Arrangement Guide from the Carpet
sources.)
- Ulrich
Sperhake wrote a tutorial outlining the first steps (PDF, 130 kB)
that one has to take to install Carpet and run an example
application.
- An explanation of the internal
workings (PDF, 120 kB) of Carpet. You should read
this if you want to modify Carpet.
- An explanation of
how scheduling works
(PDF, 120 kB) in (PUGH and) Carpet. This may be
useful for setting up mixtures of local and global operations.
- The individual Thorn Guides of Carpet. They are available
with the source code. They give details about the thorns' APIs
and user interfaces.
- Thanks to Doxygen, we now
have an overview over all
the routines and data structures in Carpet. Most individual
Doxygen tags are still missing, but the extracted documentation
is already very useful. (The online documentation might not
always be up to date; in case of doubt, extract the
documentation yourself.)
Interacting with the developers
Most discussions about Carpet, i.e. user questions, feature
requests, and bug reports, are held on the Carpet developers'
mailing list developers@lists.carpetcode.org.
You can subscribe and unsubscribe from our list management web page.
You will also find the mailing list archive there. We thank Daniel
Kobras for managing the mailing list server.
We have started to use Bugzilla to keep track of
requested features or reported bugs in Carpet. You can submit or
comment on issues from our Bugzilla pages once you
have created an account there. The old list of missing features have not
yet been moved over to Bugzilla.
Pretty pictures
Here are some pretty pictures of simulations that were
performed with Carpet:
![lapse height field](pictures/thumbnail-meudon-lapse-height.png)
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Cut through a binary black hole system. Height field of the
lapse function (approximately the time dilatation) in a binary
black hole system calculated from Meudon initial data. The
system is cut between the two black holes, so that only one
black hole is visible. The white boxes indicate the hierarchy
of refinement regions.
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![quadrupole wave](pictures/thumbnail-quadrupole.jpeg)
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A quadrupole wave. Two rotating scalar charges create a
quadrupolar wave, mimicking the gravitational wave trail of a
binary black hole system. The small bumps and riddles are
artifacts caused by the discontinuous charge distribution. To
be improved.
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![lapse isosurfaces](pictures/thumbnail-meudon-lapse-iso.png)
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Lapse isosurfaces in a binary black hole system. The same
system as above, but the lapse function is rendered as
isosurfaces.
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![velocity component](pictures/thumbnail-collapse-vel-x.png)
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A velocity component in a stellar core collapse. The x
component of the fluid velocity in a stellar core collapse.
This simulation was performed by Christian Ott.
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![error function](pictures/thumbnail-multipatch-3phi-error.jpeg)
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The error in a multipatch numerical simulation of scalar wave
propagation in a hollow spherical shell. The coarse- and fine-grid
surface show the numerical errors (computed solution - exact solution)
computed at two different resolutions, with the low resolution error
divided by 16. The fact that the two surfaces overlap nicely shows
that the errors scale as the 4th power of the grid resolution.
This simulation was performed by Jonathan Thornburg.
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![matter density](pictures/thumbnail-matter-density.jpeg)
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The fate of a proto-neutron-star bar-mode deformation.
Matter density at z=0 during the transition from an m=2 deformed star
to an m=1 deformed one. The light on the right is used to emphasizes
the spiral arms which are responsible for a small mass loss.
This simulation was performed by Gian Mario Manca.
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Moving pictures: We can show
a movie (animated gif,
3.3 MB) of a scalar wave equation with adaptive mesh
refinement. The refinement criterion is a very simplistic local
truncation error estimate. We also have
a movie (animated gif, 730 kB)
of a moving refinement region tracking a black hole.
Making sense of results
Three-dimensional time-dependent simulation results are
difficult enough to interpret when the grid is uniform. With mesh
refinement, the sheer amount of available data makes it necessary
to use professional tools to examine the data. This is not only
the case for "big physics runs", where one (should) know in
advance what to expect, but especially during development, where
things do not always go as planned. Thomas Radke was kind
enough to write an import
module for the visualisation tool OpenDX.
Related projects
Erik Schnetter
Last modified: Mon Jan 14 2008
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