The numerical treatment of problems such as partial differential equations and integral equations generally involves discretizations. In this setting a general principle may be formulated: if a domain enjoys a symmetry group, and a differential or operator equation which expresses a coordinate-free physical law is to be solved on that domain, then (if the discretization is chosen to incorporate or respect the symmetries), the resulting numerical problem (which is usually a matrix equation) is amenable to a block decomposition which greatly reduces the computational cost of determining the solution.

This research is being conducted jointly with Profs. Gene Allgower and Kurt Georg of the Department of Mathematics here at Colorado State University.