Year 1

1. Develop a prototype of the MathBus. This prototype will be used to connect locally written mesh generators to geometric modelers and finite element packages using the specifications described above. Currently Chew and Vavasis' mesh generators have different data structures and interfaces for input and output.

2. Implement a bus in which two-dimensional geometric objects can be described and annotated. We will use the Nuprl system to design these formal descriptions and annotations.

   Two-dimensional geometric objects can take many forms: they can be described by their boundaries (as parametric curves), as the solutions to inequalities involving two variables, as simplicial complexes, as convex hulls, and so on. We hope to capture as many of these representations in Nuprl/Weyl as possible. We also intend to investigate the geometric representations in commercial modeling packages like AutoCad, and describe these to the Nuprl as well.

3. Combine these tools using the MathBus to solve a finite element problem. Using the meshing tools described above, we will be able to specify the boundaries of a boundary value problem and use the MathBus to communicate these boundaries to the SPL programming language and transformation system. SPL will then use the meshing information and a specification of the partial differential equations to synthesize executable code for solving the problem using the finite element method.