This project will develop an integrated, computer graphical design tool for the numerical solution of boundary value problems over domains containing geometric features with widely varying scales. Many hours are presently spent in modeling such problems. The proposed Structural Zooming System (SZS) will significantly reduce the cost and increase the accuracy of such analyses. The central concept, as introduced here, is simple, and is coined "structural zooming." This concept approaches the problem of modeling a large complex object (the "parent" object) by recursively analyzing smaller portions ("child" objects) of the parent. Geometrical and mesh refinements may be introduced for each successive analysis. After analysis of the parent, a child is extracted. Boundary conditions derived from the parent analysis are applied to the child at the parent/child interface, and the child is analyzed. Overall accuracy is improved using an iterative algorithm involving reanalysis of both the parent and child objects to reduce disequilibrium at the interface (caused by "back-coupling" effects). Finally, the method is recursive -- a grandchild, greatgrandchild objects, etc., can be defined if responses on more refined geometrical scales are required. Phase I research will address the feasibility of structural zooming. A two-dimensional prototype, consisting of a number of distinct software modules, will be developed. Phase II will develop a completely integrated Structural Zooming System for two- and three-dimensional objects, utilizing software designs and recommendations developed during Phase I.
