CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   Edge Function methods : a more efficient alternative for 
                                 boundary value problems

SPEAKER: Jerry Dwyer, Institute of Arctic and Alpine Research 

DATE:    Wednesday, November 15, 1995

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    2:30 pm (Refreshments served at 2:15 pm)

ABSTRACT

The Edge Function method is based on the approximation of 
the solution of a boundary value problem by a linear 
combination of analytical solutions of the field equations.
The domain of interest is composed of a set of macro-elements 
(line boundaries, corners, cavities, cracks) and the analytical 
solutions are chosen to model field behavior on each
macro-element and to decay away from that element. The formulation
is based on the complex potential approach and the unknowns in the 
linear combination are chosen by matching the boundary conditions
using a boundary-Galerkin principle. The resulting system matrix
is symmetric and positive definite for traction and displacement
problems. The method has been shown to be efficient in handling 
problems with singular behavior and the number of degrees of
freedom is much lower than that required by conventional numerical
schemes. There is the added advantage over Finite Element or
Boundary Element methods that no mesh generation is required.

Accurate results have been obtained for a wide range of 
geometries with holes, cracks and mixed boundary conditions.
Application areas include rock mechanics, composite materials
and fracture mechanics.