Geometry parametric model order reduction with randomly generated projection bases

In this work, a reduced-order model for geometry parameters and fast frequency sweep is proposed. The Finite Element Method is used to solve time-harmonic Maxwell's equations. Taking into account the electromagnetic field does not arbitrarily vary as a function of frequency and geometry parameters, a low dimension system manifold is identified. Thus, the original Finite Element problem can be approximated by a model of reduced size. The basics ingredients of this approach are (1) the use of field solutions at properly selected frequencies for given geometry parameters as basis functions to project the original system, and (2) the use of a mesh deformation technique to write down the electromagnetic field upon the same mesh, i.e., preserving its topology, for different geometry parameters. This allows us to effectively take geometry parameters into account for Model-Order Reduction.