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Center for Nonlinear Studies |
This presentation develops strategies to enhance adaptive numerical methods for partial differential equation (PDE) and integral equation (IE) problems in computational electromagnetics (CEM). Through a goal-oriented emphasis, with a particular focus on scattered field and radar cross-section (RCS) quantities of interest (QoIs), we study automated acceleration techniques for the analysis of scattering targets. A primary contribution of this work, we propose an error prediction refinement strategy, which, in addition to providing rigorous global error estimates (as opposed to just error indicators), promotes equilibration of local error contribution estimates, a key requirement of efficient discretizations. Furthermore, we pursue consistent exponential convergence of the QoIs with respect to the number of degrees of freedom without prior knowledge of the solution behavior (whether smooth or otherwise) or the sensitivity of the QoIs to the discretization quality. Moreover, aside from the need for rigorous error estimation and fully-automated discretization error control, practical simulations necessitate a study of uncertain effects arising, for example, from manufacturing tolerances. Therefore, by repeating the emphasis on the QoI, we leverage the computational efforts expended in error estimation and adaptive refinement to relate perturbations in the model to perturbations of the QoI in the context of applications in CEM. This combined approach permits simultaneous control of deterministic discretization error and its effect on the QoI as well as a study of the QoI behavior in a statistical sense.
Host: Svetlana Tokareva