An arbitrary condensing, noncondensing solution strategy for large scale, multi-zone boundary element analysis

A multi-zone boundary element analysis (BEA) capability that includes substructuring and condensation in a completely general fashion is presented. This condensation procedure is shown to be an effective way to perform blocked matrix factorizations using a reduced amount of high speed computer memory, and an approach that largely removes the effect of the boundary element zone numbering scheme on the computational resources expended due to block fill-in. In iterative problems with changing configuration, the strategy of condensing (substructuring) the unchanging portion of an overall model, in an exact fashion, and subsequently iterating on the resulting reduced model, is shown to have the potential for extending the range of such iterative problems. The approach will also allow for the simultaneous condensation and subsequent expansion of multiple boundary element zones on computers with parallel processing facility. The overall algorithm is described that allows for the assembly and solution of boundary element zones connected in a quite general way that may also be arbitrarily either condensed or maintained at their original size. The approach thus allows for both condensed and uncondensed boundary element zones to consistently coexist in the same multi-zone problem. A consistent and general formulation for the treatment of the double values of traction components at boundary element zone corners is also presented. Sample problems are described to demonstrate the efficiency and usefulness of the resulting capability.