Splines and deformable surface models are widely used in computer graphics to describe free-form surfaces. These methods require manual preprocessing to discretize the surface into patches and to specify their connectivity. We present a new model of elastic surfaces based on interacting particle systems, which, unlike previous techniques, can be used to split, join, or extend surfaces without the need for manual intervention. The particles we use have long-range attraction forces and short-range repulsion forces and follow Newtonian dynamics, much like recent computational models of fluids and solids. To enable our particles to model surface elements instead of point masses or volume elements, we add an orientation to each particle's state. We devise new interaction potentials for our oriented particles which favor locally planar or spherical arrangements. We also develop techniques for adding new particles automatically, which enables our surfaces to stretch and grow. We demonstrate t...

Molecular dynamics programs simulate the behavior of biomolecular systems, leading to insights and understanding of their functions. However, the computational complexity of such simulations is enormous. Parallel machines provide the potential to meet this computational challenge. To harness this potential, it is necessary to develop a scalable program. It is also necessary that the program be easily modified by application-domain programmers. The

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 conventi...

Spectral partitioning methods use the Fiedler vector---the eigenvector of the secondsmallest eigenvalue of the Laplacian matrix---to find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on bounded-degree planar graphs and finite element meshes--- the classes of graphs to which they are usually applied. While naive spectral bisection does not necessarily work, we prove that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is O( p n) for bounded-degree planar graphs and two-dimensional meshes and O i n 1=d j for well-shaped d-dimensional meshes. The heart of our analysis is an upper bound on the second-smallest eigenvalues of the Laplacian matrices of these graphs. 1. Introduction Spectral partitioning has become one of the mos...

Motion correspondence is a fundamental problem in computer vision and many other disciplines. This article describes statistical data association techniques originally developed in the context of target tracking and surveillance and now beginning to be used in dynamic motion analysis by the computer vision community. The Mahalanobis distance measure is first introduced before discussing the limitations of nearest neighbor algorithms. Then, the track-splitting, joint likelihood, multiple hypothesis algorithms are described, each method solving an increasing-ly more complicated optimization. Real-time constraints may prohibit the application of these optimal methods. The suboptimal joint probabilistic data association algorithm is therefore described. The advantages, limitations, and relationships between the approaches are discussed. 1

this paper is as follows. In Section 2, we present some background material on general Krylov subspace methods, of which CGtype algorithms are a special case. We recall the outstanding properties of CG and discuss the issue of optimal extensions of CG to non-Hermitian matrices. We also review GMRES and related methods, as well as CG-like algorithms for the special case of Hermitian indefinite linear systems. Finally, we briefly discuss the basic idea of preconditioning. In Section 3, we turn to Lanczos-based iterative methods for general non-Hermitian linear systems. First, we consider the nonsymmetric Lanczos process, with particular emphasis on the possible breakdowns and potential instabilities in the classical algorithm. Then we describe recent advances in understanding these problems and overcoming them by using look-ahead techniques. Moreover, we describe the quasi-minimal residual algorithm (QMR) proposed by Freund and Nachtigal (1990), which uses the look-ahead Lanczos process to obtain quasi-optimal approximate solutions. Next, a survey of transposefree Lanczos-based methods is given. We conclude this section with comments on other related work and some historical remarks. In Section 4, we elaborate on CGNR and CGNE and we point out situations where these approaches are optimal. The general class of Krylov subspace methods also contains parameter-dependent algorithms that, unlike CG-type schemes, require explicit information on the spectrum of the coefficient matrix. In Section 5, we discuss recent insights in obtaining appropriate spectral information for parameter-dependent Krylov subspace methods. After that, 4 R.W. Freund, G.H. Golub and N.M. Nachtigal

We report on recent large astrophysical N-body simulations executed on the Intel Touchstone Delta system. We review the astrophysical motivation, and the numerical techniques, and discuss steps taken to parallelize these simulations. The methods scale as O(N log N), for large values of N , and also scale linearly with the number of processors. The performance, sustained for a duration of 67 hours was between 5.1 and 5.4 Gflop/sec on a 512 processor system.

In this paper we present a new algorithm for accelerating the potential calculation which occurs in the inner loop of iterative algorithms for solving electromagnetic boundary integral equations. Such integral equations arise, for example, in the extraction of coupling capacitances in three-dimensional (3-D) geometries. We present extensive experimental comparisons with the capacitance extraction code FASTCAP [1] and demonstrate that, for a wide variety of geometries commonly encountered in integrated circuit packaging, on-chip interconnect and micro-electro-mechanical systems, the new "precorrectedFFT " algorithm is superior to the fast multipole algorithm used in FASTCAP in terms of execution time and memory use. At engineering accuracies, in terms of a speed-memory product, the new algorithm can be superior to the fast multipole based schemes by more than an order of magnitude.

We discuss Inverse Spacefilling Partitioning (ISP), a partitioning strategy for nonuniform scientific computations running on distributed memory MIMD parallel computers. We consider the case of a dynamic workload distributed on a uniform mesh, and compare ISP against Orthogonal Recursive Bisection (ORB) and a Median of Medians variant of ORB, ORB-MM. We present two results. First, ISP and ORB-MM are superior to ORB in rendering balanced workloads---because they are more finegrained ---and incur communication overheads that are comparable to ORB. Second, ISP is more attractive than ORB-MM from a software engineering standpoint because it avoids elaborate bookkeeping. Whereas ISP partitionings can be described succinctly as logically contiguous segments of the line, ORB-MM's partitionings are inherently unstructured. We describe the general d-dimensional ISP algorithm and report empirical results with two- and three-dimensional, non-hierarchical particle methods. Scott B. Bad...

We describe our implementation of the parallel hashed oct-tree (HOT) code, and in particular its application to neighbor finding in a smoothed particle hydrodynamics (SPH) code. We also review the error bounds on the multipole approximations involved in treecodes, and extend them to include general cell-cell interactions. Performance of the program on a variety of problems (including gravity, SPH, vortex method and panel method) is measured on several parallel and sequential machines. 1 Introduction There are two strategies that can be applied in the quest for more knowledge from bigger and better particle simulations. One can use the brute force approach; simple algorithms on bigger and faster machines (and bigger and faster now means massively parallel). To compute the gravitational force and potential for a single interaction takes 28 floating point operations (here we count a division as 4 floating point operations and a square root as 4 floating point operations). A typical grav...