Title:  Calculus on Meshes -- Part I

                   Mathieu Desbrun
   Center for the Mathematics of Information
       California Institute of Technology

Abstract:  In this first part of a two-part lecture, we will give a crash
course in meshing. Mesh generation aims at tiling a bounded (typically 2D or
3D) domain with elements (typically triangles or tetrahedra) so that any two
of them are either disjoint or sharing a lower dimensional face. Such a
discretization of space is required for most physically-based simulation
techniques: realistic simulation of deformable objects in computer graphics,
as well as more general numerical solvers for partial differential equations
in computational science, need a discrete domain to apply finitte-element or
finite-volume methods. We will provide a brief overview of the difficulties
involved in this task, both from a theoretical point of view and in
practice. This first part will pave the way to the next lecture on the
design of an (discrete exterior) calculus on these meshes to perform all
kinds of numerical simulations.