1,444 research outputs found
Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms
We present a mathematical framework for constructing and analyzing parallel
algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting
algorithms have the capacity to simulate a wide range of spatio-temporal scales
in spatially distributed, non-equilibrium physiochemical processes with complex
chemistry and transport micro-mechanisms. The algorithms can be tailored to
specific hierarchical parallel architectures such as multi-core processors or
clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms
are controlled-error approximations of kinetic Monte Carlo algorithms,
departing from the predominant paradigm of creating parallel KMC algorithms
with exactly the same master equation as the serial one.
Our methodology relies on a spatial decomposition of the Markov operator
underlying the KMC algorithm into a hierarchy of operators corresponding to the
processors' structure in the parallel architecture. Based on this operator
decomposition, we formulate Fractional Step Approximation schemes by employing
the Trotter Theorem and its random variants; these schemes, (a) determine the
communication schedule} between processors, and (b) are run independently on
each processor through a serial KMC simulation, called a kernel, on each
fractional step time-window.
Furthermore, the proposed mathematical framework allows us to rigorously
justify the numerical and statistical consistency of the proposed algorithms,
showing the convergence of our approximating schemes to the original serial
KMC. The approach also provides a systematic evaluation of different processor
communicating schedules.Comment: 34 pages, 9 figure
MOLNs: A cloud platform for interactive, reproducible and scalable spatial stochastic computational experiments in systems biology using PyURDME
Computational experiments using spatial stochastic simulations have led to
important new biological insights, but they require specialized tools, a
complex software stack, as well as large and scalable compute and data analysis
resources due to the large computational cost associated with Monte Carlo
computational workflows. The complexity of setting up and managing a
large-scale distributed computation environment to support productive and
reproducible modeling can be prohibitive for practitioners in systems biology.
This results in a barrier to the adoption of spatial stochastic simulation
tools, effectively limiting the type of biological questions addressed by
quantitative modeling. In this paper, we present PyURDME, a new, user-friendly
spatial modeling and simulation package, and MOLNs, a cloud computing appliance
for distributed simulation of stochastic reaction-diffusion models. MOLNs is
based on IPython and provides an interactive programming platform for
development of sharable and reproducible distributed parallel computational
experiments
An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries
We review a scalable two- and three-dimensional computer code for
low-temperature plasma simulations in multi-material complex geometries. Our
approach is based on embedded boundary (EB) finite volume discretizations of
the minimal fluid-plasma model on adaptive Cartesian grids, extended to also
account for charging of insulating surfaces. We discuss the spatial and
temporal discretization methods, and show that the resulting overall method is
second order convergent, monotone, and conservative (for smooth solutions).
Weak scalability with parallel efficiencies over 70\% are demonstrated up to
8192 cores and more than one billion cells. We then demonstrate the use of
adaptive mesh refinement in multiple two- and three-dimensional simulation
examples at modest cores counts. The examples include two-dimensional
simulations of surface streamers along insulators with surface roughness; fully
three-dimensional simulations of filaments in experimentally realizable
pin-plane geometries, and three-dimensional simulations of positive plasma
discharges in multi-material complex geometries. The largest computational
example uses up to million mesh cells with billions of unknowns on
computing cores. Our use of computer-aided design (CAD) and constructive solid
geometry (CSG) combined with capabilities for parallel computing offers
possibilities for performing three-dimensional transient plasma-fluid
simulations, also in multi-material complex geometries at moderate pressures
and comparatively large scale.Comment: 40 pages, 21 figure
Research and Education in Computational Science and Engineering
Over the past two decades the field of computational science and engineering
(CSE) has penetrated both basic and applied research in academia, industry, and
laboratories to advance discovery, optimize systems, support decision-makers,
and educate the scientific and engineering workforce. Informed by centuries of
theory and experiment, CSE performs computational experiments to answer
questions that neither theory nor experiment alone is equipped to answer. CSE
provides scientists and engineers of all persuasions with algorithmic
inventions and software systems that transcend disciplines and scales. Carried
on a wave of digital technology, CSE brings the power of parallelism to bear on
troves of data. Mathematics-based advanced computing has become a prevalent
means of discovery and innovation in essentially all areas of science,
engineering, technology, and society; and the CSE community is at the core of
this transformation. However, a combination of disruptive
developments---including the architectural complexity of extreme-scale
computing, the data revolution that engulfs the planet, and the specialization
required to follow the applications to new frontiers---is redefining the scope
and reach of the CSE endeavor. This report describes the rapid expansion of CSE
and the challenges to sustaining its bold advances. The report also presents
strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie
High Performance Computing for Stability Problems - Applications to Hydrodynamic Stability and Neutron Transport Criticality
In this work we examine two kinds of applications in terms of stability and perform numerical evaluations and benchmarks on parallel platforms. We consider the applicability
of pseudospectra in the field of hydrodynamic stability to obtain more information than a
traditional linear stability analysis can provide. Furthermore, we treat the neutron transport criticality problem and highlight the Davidson method as an attractive alternative to the so far widely used power method in that context
Investigating applications portability with the Uintah DAG-based runtime system on PetaScale supercomputers
pre-printPresent trends in high performance computing present formidable challenges for applications code using multicore nodes possibly with accelerators and/or co-processors and reduced memory while still attaining scalability. Software frameworks that execute machine-independent applications code using a runtime system that shields users from architectural complexities offer a possible solution. The Uintah framework for example, solves a broad class of large-scale problems on structured adaptive grids using fluid-flow solvers coupled with particle-based solids methods. Uintah executes directed acyclic graphs of computational tasks with a scalable asynchronous and dynamic runtime system for CPU cores and/or accelerators/coprocessors on a node. Uintah's clear separation between application and runtime code has led to scalability increases of 1000x without significant changes to application code. This methodology is tested on three leading Top500 machines; OLCF Titan, TACC Stampede and ALCF Mira using three diverse and challenging applications problems. This investigation of scalability with regard to the different processors and communications performance leads to the overall conclusion that the adaptive DAG-based approach provides a very powerful abstraction for solving challenging multi-scale multi-physics engineering problems on some of the largest and most powerful computers available today
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