Connectivity as an alternative to boundary integral equations: Construction of bases.
In previous papers Herrera developed a theory of connectivity that is applicable to the problem of connecting solutions defined in different regions, which occurs when solving partial differential equations and many problems of mechanics. In this paper we explain how complete connectivity conditions can be used to replace boundary integral equations in many situations. We show that completeness is satisfied not only in steady-state problems such as potential, reduced wave equation and static and quasi-static elasticity, but also in time-dependent problems such as heat and wave equations and dynamical elasticity. A method to obtain bases of connectivity conditions, which are independent of the regions considered, is also presented.
Institute for Research in Applied Mathematics and Systems, National University of Mexico, Apdo. Postal 20-726, México 20, D.F.
I
I
Herrera
F J
FJ
Sabina