Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

/pdf/community-detection-in-graphs-34rogm3r6p.pdf

Community detection in graphs

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models. The algorithm uses iterative contractions of vertex pairs to simplify models and maintains surface error approximations using quadric matrices. By contracting arbitrary vertex pairs (not just edges), our algorithm is able to join unconnected regions of models. This can facilitate much better approximations, both visually and with respect to geometric error. In order to allow topological joining, our system also supports non-manifold surface models. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—surface and object representations

/pdf/surface-simplification-using-quadric-error-metrics-r9zm14jwq8.pdf

Surface simplification using quadric error metrics

The advent of multicore CPUs and manycore GPUs means that mainstream processor chips are now parallel systems. Furthermore, their parallelism continues to scale with Moore's law. The challenge is to develop mainstream application software that transparently scales its parallelism to leverage the increasing number of processor cores, much as 3D graphics applications transparently scale their parallelism to manycore GPUs with widely varying numbers of cores.

/pdf/scalable-parallel-programming-with-cuda-fx7qj9io5g.pdf

Scalable parallel programming with CUDA

The advent of multicore CPUs and manycore GPUs means that mainstream processor chips are now parallel systems. Furthermore, their parallelism continues to scale with Moore’s law. The challenge is to develop mainstream application software that transparently scales its parallelism to leverage the increasing number of processor cores, much as 3D graphics applications transparently scale their parallelism to manycore GPUs with widely varying numbers of cores.

https://dl.acm.org/doi/pdf/10.1145/1365490.1365500

Scalable Parallel Programming with CUDA: Is CUDA the parallel programming model that application developers have been waiting for?

Sparse matrix-vector multiplication (SpMV) is of singular importance in sparse linear algebra. In contrast to the uniform regularity of dense linear algebra, sparse operations encounter a broad spectrum of matrices ranging from the regular to the highly irregular. Harnessing the tremendous potential of throughput-oriented processors for sparse operations requires that we expose substantial fine-grained parallelism and impose sufficient regularity on execution paths and memory access patterns. We explore SpMV methods that are well-suited to throughput-oriented architectures like the GPU and which exploit several common sparsity classes. The techniques we propose are efficient, successfully utilizing large percentages of peak bandwidth. Furthermore, they deliver excellent total throughput, averaging 16 GFLOP/s and 10 GFLOP/s in double precision for structured grid and unstructured mesh matrices, respectively, on a GeForce GTX 285. This is roughly 2.8 times the throughput previously achieved on Cell BE and more than 10 times that of a quad-core Intel Clovertown system.

/pdf/implementing-sparse-matrix-vector-multiplication-on-2m98krk6l7.pdf

Implementing sparse matrix-vector multiplication on throughput-oriented processors

The massive parallelism of graphics processing units (GPUs) oers tremendous performance in many high-performance computing applications. While dense linear algebra readily maps to such platforms, harnessing this potential for sparse matrix computations presents additional challenges. Given its role in iterative methods for solving sparse linear systems and eigenvalue problems, sparse matrix-vector multiplication (SpMV) is of singular importance in sparse linear algebra. In this paper we discuss data structures and algorithms for SpMV that are eciently implemented on the CUDA platform for the ne-grained parallel architecture of the GPU. Given the memory-bound nature of SpMV, we emphasize memory bandwidth eciency and compact storage formats. We consider a broad spectrum of sparse matrices, from those that are well-structured and regular to highly irregular matrices with large imbalances in the distribution of nonzeros per matrix row. We develop methods to exploit several common forms of matrix structure while oering alternatives which accommodate greater irregularity. On structured, grid-based matrices we achieve performance of 36 GFLOP/s in single precision and 16 GFLOP/s in double precision on a GeForce GTX 280 GPU. For unstructured nite-element matrices, we observe performance in excess of 15 GFLOP/s and 10 GFLOP/s in single and double precision respectively. These results compare favorably to prior state-of-the-art studies of SpMV methods on conventional multicore processors. Our double precision SpMV performance is generally two and a half times that of a Cell BE with 8 SPEs and more than ten times greater than that of a quad-core Intel Clovertown system.

/pdf/ecient-sparse-matrix-vector-multiplication-on-cuda-421t1ah7xg.pdf

Michael Garland

Papers

Surface simplification using quadric error metrics

Scalable parallel programming with CUDA

Scalable Parallel Programming with CUDA: Is CUDA the parallel programming model that application developers have been waiting for?

Implementing sparse matrix-vector multiplication on throughput-oriented processors

Ecient Sparse Matrix-Vector Multiplication on CUDA