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.