3,470 research outputs found
A GPU-accelerated Direct-sum Boundary Integral Poisson-Boltzmann Solver
In this paper, we present a GPU-accelerated direct-sum boundary integral
method to solve the linear Poisson-Boltzmann (PB) equation. In our method, a
well-posed boundary integral formulation is used to ensure the fast convergence
of Krylov subspace based linear algebraic solver such as the GMRES. The
molecular surfaces are discretized with flat triangles and centroid
collocation. To speed up our method, we take advantage of the parallel nature
of the boundary integral formulation and parallelize the schemes within CUDA
shared memory architecture on GPU. The schemes use only
size-of-double device memory for a biomolecule with triangular surface
elements and partial charges. Numerical tests of these schemes show
well-maintained accuracy and fast convergence. The GPU implementation using one
GPU card (Nvidia Tesla M2070) achieves 120-150X speed-up to the implementation
using one CPU (Intel L5640 2.27GHz). With our approach, solving PB equations on
well-discretized molecular surfaces with up to 300,000 boundary elements will
take less than about 10 minutes, hence our approach is particularly suitable
for fast electrostatics computations on small to medium biomolecules
Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond
In this and a set of companion whitepapers, the USQCD Collaboration lays out
a program of science and computing for lattice gauge theory. These whitepapers
describe how calculation using lattice QCD (and other gauge theories) can aid
the interpretation of ongoing and upcoming experiments in particle and nuclear
physics, as well as inspire new ones.Comment: 44 pages. 1 of USQCD whitepapers
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Preparing sparse solvers for exascale computing.
Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'
Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach
We develop a rigid multiblob method for numerically solving the mobility
problem for suspensions of passive and active rigid particles of complex shape
in Stokes flow in unconfined, partially confined, and fully confined
geometries. As in a number of existing methods, we discretize rigid bodies
using a collection of minimally-resolved spherical blobs constrained to move as
a rigid body, to arrive at a potentially large linear system of equations for
the unknown Lagrange multipliers and rigid-body motions. Here we develop a
block-diagonal preconditioner for this linear system and show that a standard
Krylov solver converges in a modest number of iterations that is essentially
independent of the number of particles. For unbounded suspensions and
suspensions sedimented against a single no-slip boundary, we rely on existing
analytical expressions for the Rotne-Prager tensor combined with a fast
multipole method or a direct summation on a Graphical Processing Unit to obtain
an simple yet efficient and scalable implementation. For fully confined
domains, such as periodic suspensions or suspensions confined in slit and
square channels, we extend a recently-developed rigid-body immersed boundary
method to suspensions of freely-moving passive or active rigid particles at
zero Reynolds number. We demonstrate that the iterative solver for the coupled
fluid and rigid body equations converges in a bounded number of iterations
regardless of the system size. We optimize a number of parameters in the
iterative solvers and apply our method to a variety of benchmark problems to
carefully assess the accuracy of the rigid multiblob approach as a function of
the resolution. We also model the dynamics of colloidal particles studied in
recent experiments, such as passive boomerangs in a slit channel, as well as a
pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201
A fast multipole method for stellar dynamics
The approximate computation of all gravitational forces between
interacting particles via the fast multipole method (FMM) can be made as
accurate as direct summation, but requires less than
operations. FMM groups particles into spatially bounded cells and uses
cell-cell interactions to approximate the force at any position within the sink
cell by a Taylor expansion obtained from the multipole expansion of the source
cell. By employing a novel estimate for the errors incurred in this process, I
minimise the computational effort required for a given accuracy and obtain a
well-behaved distribution of force errors. For relative force errors of
, the computational costs exhibit an empirical scaling of . My implementation (running on a 16 core node) out-performs a
GPU-based direct summation with comparable force errors for .Comment: 21 pages, 15 figures, accepted for publication in Journal for
Computational Astrophysics and Cosmolog
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