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.

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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

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Surface simplification using quadric error metrics

Irregular computations on large workloads are a necessity in many areas of computational science. Mapping these computations to modern parallel architectures, such as GPUs, is particularly challenging because the performance often depends critically on the choice of data-structure and algorithm. In this paper, we develop a parallel processing scheme, based on Merge Path partitioning, to compute segmented row-wise operations on sparse matrices that exposes parallelism at the granularity of individual nonzero entries. Our decomposition achieves competitive performance across many diverse problems while maintaining predictable behaviour dependent only on the computational work and ameliorates the impact of irregularity. We evaluate the performance of three sparse kernels: Spiv, Spaded and Sperm. We show that our processing scheme for each kernel yields comparable performance to other schemes in many cases and our performance is highly correlated, nearly 1, to the computational work irrespective of the underlying structure of the matrices.

Optimizing Sparse Matrix Operations on GPUs Using Merge Path

A ray tracing system, method, and computer program product are provided for simultaneously traversing a hierarchy of rays and a hierarchy of objects. In operation, a hierarchy of rays and a hierarchy of objects are simultaneously traversed. Additionally, ray tracing is performed, based on the traversal.

Ray tracing system, method, and computer program product for simultaneously traversing a hierarchy of rays and a hierarchy of objects

Although modular programming is a fundamental software development practice, software reuse within contemporary GPU kernels is uncommon. For GPU software assets to be reusable across problem instances, they must be inherently flexible and tunable. To illustrate, we survey the performance-portability landscape for a suite of common GPU primitives, evaluating thousands of reasonable program variants across a large diversity of problem instances (microarchitecture, problem size, and data type). While individual specializations provide excellent performance for specific instances, we find no variants with “universally reasonable” performance. In this paper, we present a policy-based design idiom for constructing reusable, tunable software components that can be co-optimized with the enclosing kernel for the specific problem and processor at hand. In particular, this approach enables flexible granularity coarsening which allows the expensive aspects of communication and the redundant aspects of data parallelism to scale with the width of the processor rather than the problem size. From a small library of tunable device subroutines, we have constructed the fastest, most versatile GPU primitives for reduction, prefix and segmented scan, duplicate removal, reduction-by-key, sorting, and sparse graph traversal.

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Policy-based tuning for performance portability and library co-optimization

Modern GPUs are massively parallel microprocessors that can deliver very high performance for the parallel computations common in science and engineering.

Novel Architectures: Solving Computational Problems with GPU Computing

Jack Dongarra, David A. Bader, Jakub Kurzak Scientific Computing with Multicore and Accelerators

/pdf/sparse-matrix-vector-multiplication-on-multicore-and-4546un6s5r.pdf

Michael Garland

Papers

Optimizing Sparse Matrix Operations on GPUs Using Merge Path

Ray tracing system, method, and computer program product for simultaneously traversing a hierarchy of rays and a hierarchy of objects

Policy-based tuning for performance portability and library co-optimization

Novel Architectures: Solving Computational Problems with GPU Computing

Sparse Matrix-Vector Multiplication on Multicore and Accelerators