This paper presents a rapid hierarchical radiosity algorithm for illuminating scenes containing lar e polygonal patches. The afgorithm constructs a hierarchic“J representation of the form factor matrix by adaptively subdividing patches into su bpatches according to a user-supplied error bound. The algorithm guarantees that all form factors are calculated to the same precision, removing many common image artifacts due to inaccurate form factors. More importantly, the al o-rithm decomposes the form factor matrix into at most O? n) blocks (where n is the number of elements). Previous radiosity algorithms represented the element-to-element transport interactions with n2 form factors. Visibility algorithms are given that work well with this approach. Standard techniques for shooting and gathering can be used with the hierarchical representation to solve for equilibrium radiosities, but we also discuss using a brightness-weighted error criteria, in conjunction with multigrldding, to even more rapidly progressively refine the image.

We define the notion of a well-separated pair decomposition of points in d-dimensional space. We then develop efficient sequential and parallel algorithms for computing such a decomposition. We apply the resulting decomposition to the efficient computation of k-nearest neighbors and n-body potential fields.

We report on an efficient adaptive N-body method which we have recently designed and implemented. The algorithm computes the forces on an arbitrary distribution of bodies in a time which scales as N log N with the particle number. The accuracy of the force calculations is analytically bounded, and can be adjusted via a user defined parameter between a few percent relative accuracy, down to machine arithmetic accuracy. Instead of using pointers to indicate the topology of the tree, we identify each possible cell with a key. The mapping of keys into memory locations is achieved via a hash table. This allows the program to access data in an efficient manner across multiple processors. Performance of the parallel program is measured on the 512 processor Intel Touchstone Delta system. We also comment on a number of wide-ranging applications which can benefit from application of this type of algorithm.

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

Even though impressive progress has been made...

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.

BSPlib is a small communications library for bulk synchronous parallel (BSP) programming which consists of only 20 basic operations. This paper presents the full definition of BSPlib in C, motivates the design of its basic operations, and gives examples of their use. The library enables programming in two distinct styles: direct remote memory access using put or get operations, and bulk synchronous message passing. Currently, implementations of BSPlib exist for a variety of modern architectures, including massively parallel computers with distributed memory, shared memory multiprocessors, and networks of workstations. BSPlib has been used in several scientific and industrial applications; this paper briefly describes applications in benchmarking, Fast Fourier Transforms, sorting, and molecular dynamics. Key words: Bulk synchronous parallel, parallel communications library, one-sided communication. 1 Introduction Since the earliest days of computing it has been clear that, sooner or lat...

Optimizing compilers require accurate dependence testing to enable numerous, performance-enhancing transformations. However, data dependence testing is a difficult problem, particularly in the presence of pointers. Though existing approaches work well for pointers to named memory locations (i.e. other variables) , they are overly conservative in the case of pointers to unnamed memory locations. The latter occurs in the context of dynamic, pointer-based data structures, used in a variety of applications ranging from system software to computational geometry to N-body and circuit simulations. In this paper we present a new technique for performing more accurate data dependence testing in the presence of dynamic, pointer-based data structures. We will demonstrate its effectiveness by breaking false dependences that existing approaches cannot, and provide results which show that removing these dependences enables significant parallelization of a real application. 1 Introduction and Motiv...

This paper introduces an efficient two-pass rendering technique for translucent materials. We decouple the computation of irradiance at the surface from the evaluation of scattering inside the material. This is done by splitting the evaluation into two passes, where the first pass consists of computing the irradiance at selected points on the surface. The second pass uses a rapid hierarchical integration technique to evaluate a diffusion approximation based on the irradiance samples. This approach is substantially faster than previous methods for rendering translucent materials, and it has the advantage that it integrates seamlessly with both scanline rendering and global illumination methods. We show several images and animations from our implementation that demonstrate that the approach is both fast and robust, making it suitable for rendering translucent materials in production.

We present a new clustering algorithm for global illumination in complex environments. The new algorithm extends previous work on clustering for radiosity to allow for nondiffuse (glossy) reflectors. We represent clusters as points with directional distributions of outgoing and incoming radiance and importance, and we derive an error bound for transfers between these clusters. The algorithm groups input surfaces into a hierarchy of clusters, and then permits clusters to interact only if the error bound is below an acceptable tolerance. We show that the algorithm is asymptotically more efficient than previous clustering algorithms even when restricted to ideally diffuse environments. Finally, we demonstrate the performance of our method on two complex glossy environments.