Blue Gene/L represents a new way to build supercomputers, using a large number of low power processors, together with multiple integrated interconnection networks. Whether real applications can scale to tens of thousands of processors (on a machine like Blue Gene/L) has been an open question. In this paper, we describe early experience with several physics and material science applications on a 32,768 node Blue Gene/L system, which was installed recently at the Lawrence Livermore National Laboratory. Our study shows some problems in the applications and in the current software implementation, but overall, excellent scaling of these applications to 32K nodes on the current Blue Gene/L system. While there is clearly room for improvement, these results represent the first proof point that MPI applications can effectively scale to over ten thousand processors. They also validate the scalability of the hardware and software architecture of Blue Gene/L.

We describe Miranda, a massively parallel spectral/compact solver for variabledensity incompressible flow, including viscosity and species diffusivity effects. Miranda utilizes FFTs and band-diagonal matrix solvers to compute spatial derivatives to at least 10th-order accuracy. We have successfully ported this communicationintensive application to BlueGene/L and have explored both direct block parallel and transpose-based parallelization strategies for its implicit solvers. We have discovered a mapping strategy which results in virtually perfect scaling of the transpose method up to 65,536 processors of the BlueGene/L machine. Sustained global communication rates in Miranda typically run at 85% of the theoretical peak speed of the BlueGene/L torus network, while sustained communication plus computation speeds reach 2.76 TeraFLOPS. This effort represents the first time that a high-order variable-density incompressible flow solver with species diffusion has demonstrated sustained performance in the TeraFLOPS range.

Projection methods for volume rendering unstructured data work by projecting, in visibility order, the polyhedral cells of the mesh onto the image plane, and incrementally compositing each cell's color and opacity into the final image. Normally, such methods require an algorithm to determine a visibility order of the cells. The Meshed Polyhedra Visibility Order (MPVO) algorithm can provide such an order for convex meshes by considering the implications of local ordering relations between cells sharing a common face. However, in nonconvex meshes, one must also consider ordering relations along viewing rays which cross empty space between cells. In order to include these relations, the algorithm described in this paper, the scanning exact meshed polyhedra visibility ordering (SXMPVO) algorithm, scan-converts the exterior faces of the mesh and saves the ray-face intersections in an A-Buffer data structure which is then used for retrieving the extra ordering relations. The image which SXMPVO produces is the same as would be produced by ordering the cells exactly, even though SXMPVO does not compute an exact visibility ordering. This is because the image resolution used for computing the visibility ordering relations is the same as that which is used for the actual volume rendering and we choose our A-Buffer rays at the same sample points that are used to establish a polygon's pixel coverage during hardware scan conversion. Thus, the algorithm is image-space correct. The SXMPVO algorithm has several desirable features; among them are speed, simplicity of implementation, and no extra (i.e., with respect to MPVO) preprocessing.

We discuss two volume rendering methods developed at Lawrence Livermore National Laboratory. The first, cell projection, renders the polygons in the projection of each cell. It requires a global visibility sort in order to composite the cells in back to front order, and we discuss several different algorithms for this sort. The second method uses regularly spaced slice planes perpendicular to the X, Y, or Z axes, which slice the cells into polygons. Both methods are supplemented with antialiasing techniques to deal with small cells that might fall between pixel samples or slice planes, and both have been parallelized.

Direct volume rendering based on projective methods works by projecting, in visibility order, the polyhedral cells of a mesh onto the image plane, and incrementally compositing the cell’s color and opacity into the final image. Crucial to this method is the computation of a visibility ordering of the cells. If the mesh is “well‐behaved” (acyclic and convex), then the MPVO method of Williams provides a very fast sorting algorithm; however, this method only computes an approximate ordering in general datasets, resulting in visual artifacts when rendered. A recent method of Silva et al. removed the assumption that the mesh is convex, by means of a sweep algorithm used in conjunction with the MPVO method; their algorithm is substantially faster than previous exact methods for general meshes. In this paper we propose a new technique, which we call BSP‐XMPVO, which is based on a fast and simple way of using binary space partitions on the boundary elements of the mesh to augment the ordering produced by MPVO. Our results are shown to be orders of magnitude better than previous exact methods of sorting cells.

The goal of this paper is to lay a foundation for objectively comparing volume-rendered images, leading to objective evaluation of their accuracy and quality. The key elements of the foundation are: (1) a rigorous specification of all the input and parameters that need to be specified to define the conditions under which a volume-rendered image is generated; and (2) the basis for a methodology for difference classification, including a suite of functions or metrics to quantify and classify the difference between two volume-rendered images that will support an analysis of the relative importance of particular differences. The results of this method can be used to study the changes caused by modifying particular parameter values, to compare and quantify changes between images of similar data sets rendered in the same way, and to detect errors in the design, implementation or modification of a volume-rendering system. If a benchmark image is available, for example one created by a high-accuracy volume-rendering system, the method can be used to evaluate the accuracy of a given image. The key contribution of this paper is the separation of the difference into noise, bias and structured difference components. Copyright © 1999 John Wiley & Sons, Ltd.

This paper describes a volume rendering system for unstructured data, especially finite element data, that creates images with very high accuracy. The system will currently handle meshes whose cells are either linear or quadratic tetrahedra. Compromises or approximations are not introduced for the sake of efficiency. Whenever possible, exact mathematical solutions for the radiance integrals involved and for interpolation are used. The system will also handle meshes with mixed cell types: tetrahedra, bricks, prisms, wedges, and pyramids, but not with high accuracy. Accurate semi-transparent shaded isosurfaces may be embedded in the volume rendering. For very small cells, subpixel accumulation by splatting is used to avoid sampling error. A revision to an existing accurate visibility ordering algorithm is described, which includes a correction and a method for dramatically increasing its efficiency. Finally, hardware assisted projection and compositing are extended from tetrahedra to arbitrary convex polyhedra.

Various techniques are described for achieving interactive direct volume rendering of nonrectilinear data sets using fast projection (splatting) methods. The use of graphics hardware, rendering approximations, parallelization and reduced resolution meshes are discussed. Results from the use of these techniques are presented in the form of color photos and comparative timings.>

A visibility-ordering of a set of objects from some viewpoint is an ordering such that if object a obstructs object b , then b precedes a in the ordering. An algorithm is presented that generates a visibility-ordering of an acyclic convex set of meshed convex polyhedra. This algorithm takes time linear in the size of the mesh. Modifications to this algorithm and/or preprocessing techniques are described that permit nonconvex cells nonconvex meshes (meshes with cavities and/or voids), meshes with cycles, and sets of disconnected meshes to be ordered. Visibility-ordering of polyhedra is applicable to scientific visualization, particularly direct volume rendering. It is shown how the ordering algorithms can be used for domain decomposition of finite element meshes for parallel processing, and how the data structures used by these algorithms can be used to solve the spatial point location problem. The effects of cyclically obstructing polyhedra are discussed and methods for their elimination are described, including the use of the Delaunay triangulation. Methods for converting nonconvex meshes into convex meshes are described.