analysis tools. Custom code modifications can be performed using extensions to
the C programming language, like CUDA (specific to NVIDIA GPUs) and OpenCL
(multiple architectures). As graphics cards improve in reliability and
performance, cosmological N-body codes will likely take advantage of this
technology (see e.g. [413, 414, 415]), most likely in programming models that
employ hybrid algorithms for both CPUs and GPUs.

Perhaps a point of convergence between CPUs and GPUs will be in hardware such
as the Intel MIC cards (Many Integrated Core). This product, resulting from
Intel’s Larrabee research project, is essentially a GPU-CPU hybrid and
functions as a co-processor for HPC. It is expected to become available by the
end of 2012 and could become an alternative to GPUs with a simpler programming
model.

  2. ii)

Big Data

As we have seen, state of the art simulations already generate petabytes of
data. Handling this data is becoming an increasingly difficult problem and we
can only anticipate that it will get worse during the next decade. One
limiting aspect is the disk I/O speed; even with parallel distributed
filesystems (e.g. Lustre) it does not scale with the size of the
supercomputer, and thus disk I/O can take a considerable fraction of the
runtime of a simulation. Another aspect is how to manage and store extremely
large datasets, especially with collaborations commonly spread across the
world and the considerable cost of dedicated storage hardware. Simply
migrating the data from large supercomputing centers to smaller local
facilities can be difficult and time consuming.

These are serious challenges for computational cosmologists, and strategies
will need to be developed to cope with these issues. One natural development
already in practice is to merge analysis and visualization software with the
simulation code so as to reduce as much as possible the output of data during
runtime and the handling afterwards.999This is also one of the stated
development goals of the yt Project [416], http://yt-project.org/. For large
DM simulations this may mean identifying and extracting (sub)halo information,
constructing merger trees and lightcones on-the-fly, and storing only the
resulting reduced data. However, it is never possible to anticipate all the
uses of a simulation, and this motivates saving at least some full outputs.
Novel data compression techniques are a promising way forward. The idea is
that data analysis often does not require the same precision as run-time
computation. Substantial compression of the output can the be achieved either
by neglecting irrelevant bytes or by spatial averaging (a compression approach
widely used in image and video displays). For instance, the data can be stored
in a hierarchical tree fashion, where the initial bytes provide a coarse
representation of the dataset, and subsequent bytes provide refinement in
specific quantities and/or spatial regions. These would alleviate access and
reading time for postprocessing, at a cost of giving up the ability to restart
simulations and with file formats very specific to a given simulation.

The distribution of data worlwide is a serious but important problem, as
serving data products is necessary and desirable for scientific progress. In
the last few years, an increasingly popular option has been the developments
of internet databases providing reduced data products, for example from the
Millennium and MultiDark simulation databases101010http://www.mpa-
garching.mpg.de/millennium/ and http://www.multidark.org/MultiDark/. Another
alternative is to store the data itself in a distributed fashion on the
internet in the ”cloud” and using Hadoop for distributed data analysis.

####  4.3.2 Novel Approaches

  1. i)

New Gravity Solvers

Despite well-known problems with the N-body treatment of cosmological
structure formation (e.g. two body relaxation and artificial fragmentation),
there has been little progress in how to solve the collisionless Boltzmann
equation with self-gravity (Poisson-Vlasov equations). As the accuracy
demanded of cosmological simulations increases, it is likely that the short-
comings of current N-body schemes will eventually become limiting. This
motivates improvements in existing treatments, such as the introduction of
adaptive gravitational softening [417, 418] or improved density estimators
based on following the distortion of a tetrahedral tessellation of the initial
density field [419, 420], as well as radical departures from the Monte Carlo
N-body approach, such as full six-dimensional Vlasov solvers [421] or
employing kinetic theory [422].

  2. ii)

New Programming Languages - the need for parallelism

Parallelism and HPC become increasingly important also for industry and
business applications, where server farms and computing cluster with tens of
thousands of cores are now used for large-scale data mining and reduction
problems. Furthermore, since the break-down of Moore’s law for the raw core
processor performance, developers in all fields, ranging from mobile devices
to high performance cluster, need to start thinking parallel. It is therefore
not surprising that new programming languages, paradigms, and models are now
emerging, which have parallelism more naturally built in.

One example is Unified Parallel C (UPC) as an extension of the ISO C 99
programming language designed for high-performance computing on large-scale
parallel systems. This includes architectures with common global address
spaces (SMP and NUMA) and also distributed memory systems, which are more
common for cosmological applications. The main idea of UPC is to present the
developer with a single shared, partioned address space, and a Single
Instruction Multiple Data (SIMD) programming model. UPC is a specific
implementation of the more general class of PGAS (partitioned global address
space) programming languages. Other languages which follow the PGAS principles
are Co-array Fortran, Titanium, Fortress, Chapel, X10 and Global Arrays. PGAS
is based on two main concepts: multiple execution contexts with separate
address spaces and access of memory locations on one execution instance by
other execution instances. It is very likely, that in the near future
simulation codes will start using some of these language.

Besides the actual simulation software, data processing software also becomes
increasingly complex and requires efficient parallelization. Large parts of
available post-processing pipelines are programmed in general-purpose,
interpreted high-level programming languages like Python, which is slowly
replacing older IDL implementations. Both languages were essentially designed
without a particular focus on parallelism, though it is possible to use them
for parallel processing. But new languages are also arising in this field,
which will likely replace Python or IDL as the de-facto standards in the near
future. For example, Julia is new a high-level, high-performance dynamic
programming language for technical computing, which provides a sophisticated
compiler, distributed parallel execution, and an extensive mathematical
function library. Altough it is a LLVM-based just-in-time (JIT) compiler based
language it reaches nearly C/C++ performance due to heavy optimization
outperforming IDL, MATLAB, R, Python, Octave by a large factor. Most
importently it has parallelism naturally build in, which makes it suitable for
large-scale data mining and reduction on huge compute clusters.

UPC, as a PGAS parallel programming language, and Julia, as a high-performance
dynamic programming language, are just two examples and it is very likely that
the programming language landscape will move significantly more towards HPC
and parallel computing in the very near future mainly driven by industry
needs.

##  5 Conclusions

Two of the greatest mysteries of contemporary physics are the nature of dark
matter and of dark energy. As we have seen over and again in this work,
experimental and observational efforts to get at the answers to these
questions are intimately tied to predictions from cosmological DM simulations.
The simulation field, however, is rapidly evolving, as computational resources
continue to grow, enabling larger, more complicated, and more realistic
simulations to be performed. As a result, it has become more difficult for
physicists not directly involved with simulations to follow the progress of
the field, and to stay up to date with the evolving implications for studies
of DM and DE. Motivated by this realization, we have in this review attempted
to provide an overview of the current state of the field of cosmological DM
simulations, with a particular emphasis on the connection to DM detection
experiments and observational probes of DE. We have summarized the successes
and accomplishments of the current generation of simulations, but also
detailed their problems and short-comings, as well as the challenges faced by
the next generation of simulations in the coming decade.

For the DE problem, the greatest need appears to be a tremendous increase in
the number of very high resolution, very large volume, DM-only simulations,
scanning over cosmological parameters in order to allow brute-force Monte-
Carlo estimates of the parameter errors and their co-variances for future DE
surveys. At the same time, cosmic scale simulations will continue to
investigate the effects of baryonic physics, non-Gaussian initial conditions,
and modified laws of gravity.

For the DM problem, on the other hand, it seems that the DM-only approach by
itself is nearing the end of its usefulness – baryonic physics effects are
simply too important to neglect on galactic scales. There is some room for
improvement in the DM-only approach, in particular for the internal structure
of subhalos, for exploring cosmic variance and host halo mass dependency, and
for departures from the cold and collisionless DM assumption. However, the
main driver of the field must be studies of baryonic effects on the
distribution of DM in halos, since these have the potential to profoundly
alter expectations for DM detection.

The next decade promises to be filled with exciting challenges and the
potential for great discoveries. It is safe to say that the field of Numerical
Simulations of the Dark Universe will not run out of things to do.

## Acknowledgments

We are very grateful to Tom Abel, Jean-Michel Alimi, Michael Boylan-Kolchin,
Francis-Yan Cyr-Racine, Liang Gao, Phil Hopkins, Anatoly Klypin, Chung-Pei Ma,
Kristin Riebe, Graziano Rossi, Uros Seljak, Kris Sigurdson, Joachim Stadel,
Romain Teyssier, and Martin White for valuable discussions and assistance with
the simulation survey. This work has made extensive use of NASA’s Astrophysics
Data System.

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