Project: Multilevel-accelerated design-by-optimization of linear time-invariant electromagnetic systems based on physical principles, higher-order finite-element method, reduced-order and reduced-basis methods

The primary goal of this project is to unravel basic knowledge related to the concept of multilevel computer-aided design (CAD) methods which use the information on the progressively more accurate approximations of zeros and poles of linear time invariant (LTI) high-frequency passive electromagnetic systems, governed by partial differential equations, obtained from time consuming simulations based on physical principles using a higher-order finite-element method (FEM). The project will propose, verify, and assess the efficiency, and other merits of new high-accuracy algorithms which employ the new multilevel concept. The end result will be to discover and verify new methodologies and develop prototypes of numerical tools which would fundamentally lower the computational cost associated with computer aided design based on numerical modeling and simulation using physical principles for a broad class of electromagnetic problems.

The project emphasizes the input-output system view at the considered boundary-value problems derived from Maxwell’s equations, including the pole-zero LTI system representation, as a framework for novel and efficient analysis strategies. It will be shown that this new view in high-frequency CAD enables one to apply model order reduction (MOR) techniques at various stages of the problem solution and optimization, to develop efficient goal-oriented model order reduction for components characterized by scattering parameters, as well as to specify design goals and develop effective optimization strategies focused on zeros and poles, and their derivatives.