We propose a new algorithm for constructing finite-element meshes suitable for spacetime discontinuous Galerkin solutions of linear hyperbolic PDEs. Given a triangular mesh of some planar domain# and a target time value T , our method constructs a tetrahedral mesh of the spacetime domain [0, T] in constant running time per tetrahedron in IR using an advancing front method. Elements are added to the evolving mesh in small patches by moving a vertex of the front forward in time. Spacetime discontinuous Galerkin methods allow the numerical solution within each patch to be computed as soon as the patch is created. Our algorithm employs new mechanisms for adaptively coarsening and refining the front in response to a posteriori error estimates returned by the numerical code. A change in the front induces a corresponding refinement or coarsening of future elements in the spacetime mesh. Our algorithm adapts the duration of each element to the local quality, feature size, and degree of refinement of the underlying space mesh. We directly exploit the ability of discontinuous Galerkin methods to accommodate discontinuities in the solution fields across element boundaries.

Computational simulation of time-varying physical processes is of fundamental importance for many scientific and engineering applications. Most frequently, time-varying simulations are performed over multiple spatial grids at discrete points in time. We investigate a new approach to time-varying simulation: spacetime discontinuous Galerkin finite element methods. The result of this simulation method is a simplicial tessellation of spacetime with per-element polynomial solutions for physical quantities such as strain, stress, and velocity. To provide accurate visualizations of the resulting solutions, we have developed a method for per-pixel evaluation of solution data on the GPU. We demonstrate the importance of per-pixel rendering versus simple linear interpolation for producing high quality visualizations. We also show that our system can accommodate reasonably large datasets - spacetime meshes containing up to 20 million tetrahedra are not uncommon in this domain.

The visualization and application steering environment (VASE) provides interactive visual computing and steering for scientific and engineering programs. VASE defines an abstraction for a steerable program structure and provides tools that create and manage collections of these steerable codes. It is designed to work with existing codes written in Fortran. Based on simple annotations in the source code, VASE tools construct a high-level model of each application and enable the user to work with this model rather than at the detailed source-code level. Collections of steerable codes execute in a distributed environment. This paper describes the design objectives for VASE, its architecture, and its implementation, and illustrates its use with an example application.

A mathematical data model for scientific visualization that is based on the mathematics of fiber bundles is presented. Previous results are extended to the case of piecewise field representations (associated with grid-based data representations), and a general mathematical model for piecewise representations of fields on irregular grids is presented. The various types of regularity that can be found in computational grids and techniques for compact field representation based on each form of regularity are discussed. These techniques can be combined to obtain efficient methods for representing fields on grids with various regular or partially regular structures.>