ITR/AP: Multiscale Models for Microstructure Simulation and Process Design:
- Overview
- Cross-discipline research leads to powerful new analysis method
- Research on software environments sparks new science
- Interdisciplinary training of engineers, scientists & mathematicians
We are developing a new class of space-time discontinuous Galerkin (SDG) finite element methods for solving hyperbolic problems in science and engineering. These methods offer many advantages—but they require new finite element formulations and new techniques for mesh generation, visualization and parallel computing to realize their full potential. Our cross-disciplinary research effort yielded a powerful new analysis tool.
SDG solutions are computed on unstructured spacetime meshes that satisfy a causality constraint that enables an O(N) solution process. Our computational geometry group developed the Tent-Pitcher algorithm to meet this requirement, with support for adaptive mesh refinement (Figs. 1, 2).
Fig. 1: Adaptive spacetime mesh reveals fine details of shockwave trajectories in crack-tip wave scattering example. Solution data projected onto the transparent constant-time planes generated the animation frames shown below.
Fig. 2: Tent Pitcher generates causal spacetime meshes that can be solved patch by patch in O(N) time.
Data computed on unstructured spacetime grids requires new visualization technology. Our visualization team developed new data extraction methods and used the latest generation of graphics hardware to implement interactive tools to produce per-pixel-accurate renderings of our solution data (Fig. 3).
Fig. 3: Per-pixel accurate rendering reveals fine detail of high-resolution SDG solutions. We use the programmable capabilities of contemporary graphics hardware to attain interactive rates.
