We are building a prototype to perform moving mesh
simulations in the Lagrangian framework. Our meshes are built
of Bezier triangles and object boundaries are represented in terms
of B-spline curves. As the mesh moves we keep track of object
boundaries, and modify it to keep it well shaped by applying the
operations of edge flipping, vertex insertion and deletion, and
curve smoothing. We discuss a calculus of geometric primitives
for Bezier curves and triangles that we employ to implement the
above operations. In addition we discuss the organization and
key components of our prototype, and present experimental results.

Our target application is Navier-Stokes blood flow simulations in three dimensions, here we focus first on two-dimensional simulations, utilizing many procedures which generalize well to higher dimension applications. The system is designed for any fixed-order Bezier elements and B-Splines. In this work we have concentrated on quadratics, although most of the operations are valid for any order elements. The current simulations are based on convection equations rather than Navier-Stokes for simplicity.

Other Mini-PROBEs for Summer 2003

Algorithms for Facility Location

Anonymous Communication

Designing Overlay Multicast Networks for Streaming

Dynamic Algorithms

HumanAUT

Space-Efficient
Point Location