In the last decades cosmological N-body dark matter simulations have enabled ab initio studies of the formation of structure in the Universe. Gravity amplified small density fluctuations generated shortly after the Big Bang, leading to the formation of galaxies in the cosmic web. These calculations have led to a growing demand for methods to analyze time-dependent particle based simulations. Rendering methods for such N-body simulation data usually employ some kind of splatting approach via point based rendering primitives and approximate the spatial distributions of physical quantities using kernel interpolation techniques, common in SPH (Smoothed Particle Hydrodynamics)-codes. This paper proposes three GPU-assisted rendering approaches, based on a new, more accurate method to compute the physical densities of dark matter simulation data. It uses full phase-space information to generate a tetrahedral tessellation of the computational domain, with mesh vertices defined by the simulation's dark matter particle positions. Over time the mesh is deformed by gravitational forces, causing the tetrahedral cells to warp and overlap. The new methods are well suited to visualize the cosmic web. In particular they preserve caustics, regions of high density that emerge, when several streams of dark matter particles share the same location in space, indicating the formation of structures like sheets, filaments and halos. We demonstrate the superior image quality of the new approaches in a comparison with three standard rendering techniques for N-body simulation data.

For quantitative examination of phenomena that simultaneously occur on very different spatial and temporal scales, adaptive hierarchical schemes are required. A special numerical multilevel technique, associated with a particular hierarchical data structure, is so-called adaptive mesh refinement (AMR). It allows one to bridge a wide range of spatial and temporal resolutions and therefore gains increasing popularity. We describe the interplay of several visualization and VR software packages for rendering time dependent AMR simulations of the evolution of the first star in the universe. The work was done in the framework of a television production for Discovery Channel television, "The Unfolding Universe.". Parts of the data were taken from one of the most complex AMR simulation ever carried out: It contained up to 27 levels of resolution, requiring modifications to the texture based AMR volume rendering algorithm that was used to depict the density distribution of the gaseous interstellar matter. A voice and gesture controlled CAVE application was utilized to define camera paths following the interesting features deep inside the computational domains. Background images created from cosmological computational data were combined with the final renderings.

As an entry for the 2001 Gordon Bell Award in the special category, we describe our 3-d, hybrid, adaptive mesh refinement (AMR) code Enzo designed for high-resolution, multiphysics, cosmological structure formation simulations. Our parallel implementation places no limit on the depth or complexity of the adaptive grid hierarchy, allowing us to achieve unprecedented spatial and temporal dynamic range. We report on a simulation of primordial star formation which develops over 8000 subgrids at 34 levels of refinement to achieve a local refinement of a factor of 1012 in space and time. This allows us to resolve the properties of the first stars which form in the universe assuming standard physics and a standard cosmological model. Achieving extreme resolution requires the use of 128-bit extended precision arithmetic (EPA) to accurately specify the subgrid positions. We describe our EPA AMR implementation on the IBM SP2 Blue Horizon system at the San Diego Supercomputer Center.