Numerical Optimization of Multifunctional Components

Abstract : Engineering components are increasingly complex in composition and structure and increasingly multifunctional. Indeed, it is only through complexity and multifunctionality that the defense industry can satisfy the stringent performance requirements associated with critical defense applications. However, these complex, multifunctional systems no longer admit intuitive analysis of trade-off considerations. Industries must pursue optimization, including optimal choice of material, configuration, and deployment to realize the potential of these new approaches. The essential mathematical enabler, and the focus of this project, is very fast yet reliable prediction of component behavior. Armed with the latter, industries may pursue extensive optimization and even real-time adaptive design and control. The critical ingredients of this approach are as follows: (1) reduced-basis approximations to effect significant reduction in state-space dimensionality, (2) "a posteriori" error bounds to provide rigorous error estimation and control, and (3) offline/online computational decompositions to permit rapid evaluation of output bounds in the limit of many queries. In this project, the authors extend this basic methodology to noncoercive, non-affine, non-linear, and non-elliptic (parabolic) problems. This will allow them to address the full range of disciplines that typically describe thermal, structural, fluidic, acoustic, and electromagnetic multifunctional components. Five conferences and seven related publications are listed. (23 refs.)