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

We present a strictly balanced method for the parallel computation of sparse matrix-vector products (SpMV). Our algorithm operates directly upon the Compressed Sparse Row (CSR) sparse matrix format without preprocessing, inspection, reformatting, or supplemental encoding. Regardless of nonzero structure, our equitable 2D merge-based decomposition tightly bounds the workload assigned to each processing element. Furthermore, our technique is suitable for recursively partitioning CSR datasets themselves into multi-scale, distributed, NUMA, and GPU environments that are constrained by fixed-size local memories. We evaluate our method on both CPU and GPU microarchitectures across a very large corpus of diverse sparse matrix datasets. We show that traditional CsrMV methods are inconsistent performers, often subject to order-of-magnitude performance variation across similarly-sized datasets. In comparison, our method provides predictable performance that is substantially uncorrelated to the distribution of nonzeros among rows and broadly improves upon that of current CsrMV methods.

Merge-based parallel sparse matrix-vector multiplication

Modern microprocessors are becoming increasingly parallel devices, and GPUs are at the leading edge of this trend. Designing parallel algorithms for manycore chips like the GPU can present interesting challenges, particularly for computations on sparse data structures. One particularly common example is the collection of sparse matrix solvers and combinatorial graph algorithms that form the core of many physical simulation techniques. Although seemingly irregular, these operations can often be implemented with data parallel operations that map very well to massively parallel processors.

Sparse matrix computations on manycore GPU's

Motion is the center of attention in many applications of computer graphics. Skeletal motion for articulated characters can be processed and altered in a variety of ways to increase the versatility of each motion clip. However, analogous techniques have not yet been developed for free-form deforming surfaces like cloth and faces. Given the time-consuming nature of producing each free-form motion clip, the ability to alter and reuse free-form motion would be very desirable. We present a novel method for processing free-form motion that opens up a broad range of possible motion alterations including motion blending, keyframe insertion, and temporal signal processing. Our method is based on a simple yet powerful differential surface representation that is invariant under rotation and translation and which is well suited for surface editing in both space and time.

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Free-form motion processing

Time-varying surfaces are ubiquitous in movies, games, and scientific applications. For reasons of efficiency and simplicity of formulation, these surfaces are often generated and represented as dense polygonal meshes with static connectivity. As a result, such deforming meshes often have a tremendous surplus of detail, with many more vertices and polygons than necessary for any given frame. An extensive amount of work has addressed the issue of simplifying a static mesh: however, these methods are inadequate for time-varying surfaces when there is a high degree of non-rigid deformation. We thus propose a new multiresolution representation for deforming surfaces that, together with our dynamic improvement scheme, provides high quality surface approximations at any level-of-detail, for all frames of an animation. Our algorithm also gives rise to a new progressive representation for time-varying multiresolution hierarchies, consisting of a base hierarchy for the initial frame and a sequence of update operations for subsequent frames. We demonstrate that this provides a very effective means of extracting static or view-dependent approximations for a deforming mesh over all frames of an animation.

/pdf/progressive-multiresolution-meshes-for-deforming-surfaces-zqp8f6eu75.pdf

Progressive multiresolution meshes for deforming surfaces

Techniques for interactive deformation of unstructured polygon meshes are of fundamental importance to a host of applications. Most traditional approaches to this problem have emphasized precise control over the deformation being made. However, they are often cumbersome and unintuitive for non-expert users.In this paper, we present an interactive system for deforming unstructured polygon meshes that is very easy to use. The user interacts with the system by sketching curves in the image plane. A single stroke can define a free-form skeleton and the region of the model to be deformed. By sketching the desired deformation of this reference curve, the user can implicitly and intuitively control the deformation of an entire region of the surface. At the same time, the reference curve also provides a basis for controlling additional parameters, such as twist and scaling. We demonstrate that our system can be used to interactively edit a variety of unstructured mesh models with very little effort. We also show that our formulation of the deformation provides a natural way to interpolate between character poses, allowing generation of simple key framed animations.

Michael Garland

Papers

Merge-based parallel sparse matrix-vector multiplication

Sparse matrix computations on manycore GPU's

Free-form motion processing

Progressive multiresolution meshes for deforming surfaces

Sketching mesh deformations