The NIH/NIGMS
Center for Integrative Biomedical Computing

A variety of application domains from geophysics to bio-medicine employ some form of a Hamilton-Jacobi (H-J) mathematical model, as these models provide a natural means of expressing conservation properties. The two most prevalent H-J models seen in the literature are the Eikonal equation (a static H-J model based upon Fermat's Principle for determining minimal paths) and the Level-Set equations (a time-dependent H-J model used for addressing moving interface problems). Both of these sets of equations can be solved very efficiently on structured (lattice) meshes with appropriate upwind-based finite difference schemes. In addition, great strides have been made to map efficient CPU-focused structured mesh H-J formulations to commodity-based streaming architectures such as GPUs. However, many application scientists desire to use H-J formulations because of their conservation properties while at the same time their applications require the use of unstructured meshes because of the meed for geometric-modeling fidelity (for both boundaries and interfaces). Although H-J formulations exist in part for unstructured meshes, their mapping to GPUs is non-trivial due to the indexing (and corresponding data-structures) necessary for non-lattice meshes.

The goal of this work is to develop, test, document and distribute a collection of software tools for efficiently solving several classes of equations of H-J type - in particular, Eikonal (minimal path) equations and level-set equations - on unstructured (triangular and tetrahedral) meshes using commodity streaming architectures. As the project progresses, we will add additional PDE-based solvers (and support code) that require similar combinations of unstructured mesh methods (e.g. FEM) and the use of streaming architectures.